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European Mathematical Society Publishing House
2024-03-29 10:43:09
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=30&update_since=2024-03-29
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
30
1994
1
On Non-real Eigenvalues of Schrödinger Operators in a Weighted Hilbert Space
Masaharu
Arai
Nihon University, TOKYO, JAPAN
Osanobu
Yamada
Kyoto University, KYOTO, JAPAN
Partial differential equations
General
1
14
10.2977/prims/1195166274
http://www.ems-ph.org/doi/10.2977/prims/1195166274
Quantized Enveloping Algebras Associated with Simple Lie Superalgebras and Their Universal R-matrices
Hiroyuki
Yamane
Osaka University Graduate School of Science, OSAKA, JAPAN
Nonassociative rings and algebras
General
15
87
10.2977/prims/1195166275
http://www.ems-ph.org/doi/10.2977/prims/1195166275
Generalised Mean Averaging Interpolation by Discrete Cubic Splines
Manjulata
Shrivastava
R.D. University, JABALPUR, INDIA
The aim of this work is to introduce for a discrete function, certain discrete integrals which may reduce in particular to usual Riemann Stieltjes integrals. We name them as Discrete Stieltjes integrals. The existence and convergence of a discrete cubic interpolatory spline whose discrete Stieltjes integrals between consecutive meshpoints match with the corresponding integrals of a given periodic discrete function, are studied.
Approximations and expansions
General
89
95
10.2977/prims/1195166276
http://www.ems-ph.org/doi/10.2977/prims/1195166276
The Singularities of Type Ak of Holonomic Systems
Nguyen
Dai
Institute of Mathematics, HANOI, VIETNAM
Partial differential equations
General
97
109
10.2977/prims/1195166277
http://www.ems-ph.org/doi/10.2977/prims/1195166277
Quantized Radiation States from the Infinite Dicke Model
Reinhard
Honegger
Universität Tübingen, TÜBINGEN, GERMANY
Alfred
Rieckers
Universität Tübingen, TÜBINGEN, GERMANY
By interpreting infinitely many two-level atoms as a mean field quantum lattice system in a recent paper the time evolution of the Dicke Maser model has been elaborated in terms of operator algebraic methods. Using these results, here the emitted radiation of the infinite Dicke model is investigated. It is shown how the collective behaviour of the atoms influences the quantized radiation, which for large times becomes classically coherent (in the sense of Glauber). The field modes which are (approximately) resonant with the level-splitting energy of the atoms are found to be the essential part of the generated coherent light, and thereby determine its macroscopic nature. Furthermore, the destruction and revival of coherence, the mean number of the emitted photons during the time evolution, as well as their spatial distribution are discussed.
Functional analysis
General
111
138
10.2977/prims/1195166278
http://www.ems-ph.org/doi/10.2977/prims/1195166278
Existence of the Greek Letter Elements in the Stable Homotopy Groups of E(n)*-Localized Spheres
Katsumi
Shimomura
Kochi University, KOCHI, JAPAN
Masaaki
Yokotani
Okayama University, OKAYAMA, JAPAN
Let E2*.*(X) denote the E2-term of the Adams-Novikov spectral sequence converging to the homotopy groups of X. We can define the Greek letter elements in E2*.*(LnS0) in the same way as those in E2*.*(S0). We show that these of E2*.*(LnS0) are permanent cycles, though we know little for E2*.*(S0).
Algebraic topology
General
139
150
10.2977/prims/1195166279
http://www.ems-ph.org/doi/10.2977/prims/1195166279
The E7 Commuting Squares Produce D10 as Principal Graph
David
Evans
University of Wales Cardiff, CARDIFF, UNITED KINGDOM
Yasuyuki
Kawahigashi
University of Tokyo, TOKYO, JAPAN
We prove that the (two) connections, or commuting squares, on the Coxeter-Dynkin diagram E7 produce a subfactor with principal graph D10. This was conjectured by J.-B. Zuber in connection with modular invariants in conformal field theory, and solve the last case of computing the flat parts of the connections on Coxeter-Dynkin diagrams with index less than 4.
Functional analysis
General
151
166
10.2977/prims/1195166280
http://www.ems-ph.org/doi/10.2977/prims/1195166280
2
Solvability of Convolution Operators
Yasunori
Okada
Chiba University, CHIBA, JAPAN
We study the Surjectivity of convolution operators on the spaces of hyperfunctions and Fourier hyperfunctions. On the space of hyperfunctions, we give a sufficient condition (the kernel is a nonzero ultradistribution), weaker than earlier conditions. On the space of Fourier hyperfunction, we give a new sufficient condition and new necessary conditions for the Surjectivity. Especially in one dimensional case, they become a sufficient and necessary condition. To this aim we use the Fourier analysis as in L. Ehrenpreis [E-2] and T. Kawai [Ka-1].
Fourier analysis
General
167
190
10.2977/prims/1195166127
http://www.ems-ph.org/doi/10.2977/prims/1195166127
Representations of Witt Algebras
Senapathi
Rao
Tata Institute of Fundamental Research, BOMBAY, INDIA
In this paper we construct new families of representations for the Lie-algebra of diffeomorphisms of the torus Td and describe its sub representations.
Nonassociative rings and algebras
General
191
201
10.2977/prims/1195166128
http://www.ems-ph.org/doi/10.2977/prims/1195166128
A Characterization for Fourier Hyperfunctions
Jaeyoung
Chung
Kunsan National University, KUNSAN, SOUTH KOREA
Soon-Yeong
Chung
Sogang University, SEOUL, SOUTH KOREA
Dohan
Kim
Seoul National University, SEOUL, SOUTH KOREA
The space of test functions for Fourier hyperfunctions is characterized by two conditions sup |φ (x)| exp k|x|
Functional analysis
General
203
208
10.2977/prims/1195166129
http://www.ems-ph.org/doi/10.2977/prims/1195166129
PBW Basis of Quantized Universal Enveloping Algebras
Yoshihisa
Saito
University of Tokyo, TOKYO, JAPAN
Nonassociative rings and algebras
General
209
232
10.2977/prims/1195166130
http://www.ems-ph.org/doi/10.2977/prims/1195166130
Oriented Z4 Actions without Stationary Points
Tamio
Hara
Tokyo University of Science, CHIBA-KEN, JAPAN
Manifolds and cell complexes
General
233
248
10.2977/prims/1195166131
http://www.ems-ph.org/doi/10.2977/prims/1195166131
Operators Characterized by Certain Cauchy-Schwarz Type Inequalities
Hideharu
Watanabe
Kyushu University, FUKUOKA, JAPAN
A Hilbert space operator T satisfying either (**) |(T ξ, η)|2 ≤ (|T| ξ,ξ) (|T| η,η) for all ξ, η ∈ ℋ, or (*) |(T ξ, ξ)| ≤ (|(T|ξ,ξ) for all ξ ∈ ℋ, is studied. The condition (**) defines a slightly larger class than the hyponormality, and for compact operators (**) is equivalent to the normality. The condition (*) is characterized by using an operator whose numerical radius is less than 1, and among other things we show that (*) and the normality are equivalent for matrices. Moreover, we show that (*) and the normality are equivalent for trace class operators in Appendix.
Operator theory
General
249
259
10.2977/prims/1195166132
http://www.ems-ph.org/doi/10.2977/prims/1195166132
Fibrewise Hopf Construction and Hoo Formula for Pairings
Nobuyuki
Oda
Fukuoka University, FUKUOKA, JAPAN
Let Γ be a fibrewise co-Hopf space over a topological space B. A ΓB-suspension space ΓBX is a generalization of a fibrewise suspension space ΣBX for any fibrewise pointed space X over B. Making use of ΓB-suspension space, we define ΓB-Hopf construction and prove a ΓB-suspension formula which generalizes the suspension formula of C. S. Hoo. The dual formula is also proved.
Algebraic topology
General
261
279
10.2977/prims/1195166133
http://www.ems-ph.org/doi/10.2977/prims/1195166133
Fibrewise Decomposition of Generalized Suspension Spaces and Loop Spaces
Nobuyuki
Oda
Fukuoka University, FUKUOKA, JAPAN
We work in the category TopBB of fibrewise pointed topological spaces over B. Let Γ be a co-Hopf space (which need not be co-associative) in TopBB. The ΓB-suspension space ΓBX and the ΓB-loop space Γ*BX of a fibrewise pointed space X over B are defined as generalization of the usual suspension space ΣX and the loop space ΩX respectively, ΓB-suspension spaces and ΓB-loop spaces have some properties similar to those of the usual suspension spaces and loop spaces. This is an example of Eckmann-Hilton duality. In this paper, decomposition theorems of ΓB-suspension space ΓBX and ΓB-loop space Γ*BX are proved. Short exact sequences of homotopy sets involving ΓB-suspension spaces or ΓB-loop spaces are obtained in the category of algebraic loops.
Algebraic topology
General
281
295
10.2977/prims/1195166134
http://www.ems-ph.org/doi/10.2977/prims/1195166134
A Process Associated with the Radially Symmetric Dirac Equation
Brian
Jefferies
University of New South Wales, SYDNEY, AUSTRALIA
The dynamical group associated with the Dirac equation with a radially symmetric potential is represented in terms of integrals with respect to the operator valued set functions associated with the Dirac equation in four space-time dimensions.
Quantum theory
General
297
325
10.2977/prims/1195166135
http://www.ems-ph.org/doi/10.2977/prims/1195166135
Classical Theta Functions and Quantum Tori
Alan
Weinstein
University of California, BERKELEY, UNITED STATES
The Schwartz kernel of the multiplication operation on a quantum torus is shown to be the distributional boundary value of a classical multivariate theta function. The kernel satisfies a Schrödinger equation in which the role of time is played by the deformation parameter ℏ and the role of the hamiltonian by a Poisson structure. At least in some special cases, the kernel can be written as a sum of products of single variable theta functions.
Quantum theory
General
327
333
10.2977/prims/1195166136
http://www.ems-ph.org/doi/10.2977/prims/1195166136
Indecomposable Restricted Representations of Quantum sl2
Vyjayanthi
Chari
University of California, RIVERSIDE, UNITED STATES
Alexander
Premet
The University of Manchester, MANCHESTER, UNITED KINGDOM
We construct and classify all the indecomposable restricted representations of Uq(sl2 when q is a root of unity.
Nonassociative rings and algebras
General
335
352
10.2977/prims/1195166137
http://www.ems-ph.org/doi/10.2977/prims/1195166137
3
Highest Weight Modules and bFunctions of Semi-invariants
Akihiko
Gyoja
Kyoto University, KYOTO, JAPAN
Topological groups, Lie groups
General
353
400
10.2977/prims/1195165904
http://www.ems-ph.org/doi/10.2977/prims/1195165904
The Structure of Hilbert Flag Varieties
Gerard
Helminck
Universiteit Twente, ENSCHEDE, NETHERLANDS
Aloysius
Helminck
North Carolina State University, RALEIGH, UNITED STATES
In this paper we present a geometric realization of infinite dimensional analogues of the finite dimensional representations of the general linear group. This requires a detailed analysis of the structure of the flag varieties involved and the line bundles over them. In general the action of the restricted linear group can not be lifted to the line bundles and thus leads to central extensions of this group. It is determined exactly when these extensions are non-trivial. These representations are of importance in quantum field theory and in the framework of integrable systems. As an application, it is shown how the flag varieties occur in the latter context.
Topological groups, Lie groups
General
401
441
10.2977/prims/1195165905
http://www.ems-ph.org/doi/10.2977/prims/1195165905
Small Resolutions of Schubert Varieties in Symplectic and Orthogonal Grassmannians
Parameswaran
Sankaran
, CHENNAI, INDIA
P.
Vanchinathan
, CHENNAI, INDIA
Algebraic geometry
General
443
458
10.2977/prims/1195165906
http://www.ems-ph.org/doi/10.2977/prims/1195165906
Yangians and Gelfand-Zetlin Bases
Maxim
Nazarov
University of Wales Swansea, SWANSEA, UNITED KINGDOM
Vitaly
Tarasov
Steklov Mathematical Institute, ST. PETERSBURG, RUSSIAN FEDERATION
We establish a connection between the modern theory of Yangians and the classical construction of the Gelfand-Zetlin bases for the Lie algebra gln. Our approach allows us to produce the q-analogues of the Gelfand-Zetlin formulae in a straightforward way.
Nonassociative rings and algebras
General
459
478
10.2977/prims/1195165907
http://www.ems-ph.org/doi/10.2977/prims/1195165907
Quantization in Polar Coordinates and the Phase Operator
Daniel
Dubin
Open University, MILTON KEYNES, UNITED KINGDOM
Mark
Hennings
Rugby School, RUGBY, UNITED KINGDOM
Thomas
Smith
Open University, MILTON KEYNES, UNITED KINGDOM
We review some of the difficulties previously encountered in defining the phase operator for finite quantum systems. We then propose the Wigner-Weyl quantization of the angle function φ on phase space as the phase operator, and derive a closed expression for its matrix elements with respect to the Hermite functions. We also determine the quantization of elφ, which turns out to be a weighted shift operator, its spectrum and that of its adjoint. This is done in the framework of quantization of a certain symbol class of phase space distributions, specialized to those which depend on one variable only. After recalling some results for the position and momentum variables, we apply the scheme to functions of radius or angle. We give necessary and sufficient conditions for operators obtained by quantizing functions of the angle to be elements of ℒ+ [S(R)] and ℒ+ [S(R), L2(R)], and a sufficient condition for boundedness. We then consider the associated questions of commutation relations and uncertainties for operators in ℒ+ [S(R), L2(R)], which we define as bilinear forms. As must be the case, the commutator between our phase operator and the number operator exhibits noncanonical terms. Not surprisingly, the Poisson bracket of their phase space symbols also exhibits a noncanonical term.
Quantum theory
Functional analysis
General
479
532
10.2977/prims/1195165908
http://www.ems-ph.org/doi/10.2977/prims/1195165908
4
Erratum to 'Non-Hypoellipticity for Degenerate Elliptic Operators'
Yoshinori
Morimoto
Kyoto University, KYOTO, JAPAN
Partial differential equations
Functional analysis
General
533
534
10.2977/prims/1195165789
http://www.ems-ph.org/doi/10.2977/prims/1195165789
Cyclic Generalized Vectors for Algebras of Unbounded Operators
Atsushi
Inoue
Hiroshima University, HIROSHIMA, JAPAN
W.
Karwowski
Uniwersytet Wroclawski, WROCLAW, POLAND
Operator theory
General
577
601
10.2977/prims/1195165790
http://www.ems-ph.org/doi/10.2977/prims/1195165790
A Generalized Grothendieck-RIemann-Roch Theorem for Hirzebruch's χy-Characteristic and Ty-Characteristic
Shoji
Yokura
Kagoshima University, KAGOSHIMA, JAPAN
Algebraic geometry
General
603
610
10.2977/prims/1195165791
http://www.ems-ph.org/doi/10.2977/prims/1195165791
Remarks on the Bifurcation of Two Dimensional Capillary-Gravity Waves of Finite Depth
Hisashi
Okamoto
Kyoto University, KYOTO, JAPAN
Mayumi
Shoji
Nihon University, TOKYO, JAPAN
We consider the problem to determine the two dimensional water waves of permanent configuration. The problem is a bifurcation problem ([16]). In this paper, we define a mapping G between two Hilbert spaces and prove that the solutions of the above problem are in one-to-one correspondence to the zeros of the mapping G. Our most important contribution in this paper is to clarify the role of the aspect ratio, i.e., the ratio between the mean depth of the flow and the wave length. In particular, we prove that there is no degenerate bifurcation point, whatever the aspect ratio may be.
Fluid mechanics
General
611
640
10.2977/prims/1195165792
http://www.ems-ph.org/doi/10.2977/prims/1195165792
On the Cones of α- and Generalized α-Positivity for Quantum Field Theories with Indefinite Metric
Gerald
Hofmann
HTWK Leipzig, LEIPZIG, GERMANY
In order to construct a Krein-space theory (i.e., a *-algebra of (unbounded) operators which are defined on a common, dense, and invariant domain in a Krein space) the cones of α-positivity and generalized α-positivity are considered in tensor algebras. The relations between these cones, algebraic #-cones, and involutive cones are investigated in detail. Furthermore, an example of a P-functional ϕ defined on (C2)⊗ (tensor algebra over C2) not being α-positive and yielding a non-trivial Krein-space theory is explicitely constructed. Thus, an affirmative answer to the question whether or not the method of P-functionals (introduced by Ôta) is more general than the one of α-positivity (introduced by Jakóbczyk) is provided in the case of tensor algebras.
Functional analysis
General
641
670
10.2977/prims/1195165793
http://www.ems-ph.org/doi/10.2977/prims/1195165793
On the Irregularity of Special Non-Canonical Surfaces
Kazuhiro
Konno
Osaka University, OSAKA, JAPAN
We consider minimal surfaces of general type whose canonical map is "special" meaning that it is composed of a pencil or its degree is high. We characterize, to some extent, Beauville's examples of irregularity 2 in the pencil case, and show that the irregularity is at most 12 when the canonical degree is 5.
Algebraic geometry
General
671
688
10.2977/prims/1195165794
http://www.ems-ph.org/doi/10.2977/prims/1195165794
Rings of Fractions of B (H)
Yoshinobu
Kato
Nagaikeso Institute, OSAKA, JAPAN
Operator theory
General
689
693
10.2977/prims/1195165795
http://www.ems-ph.org/doi/10.2977/prims/1195165795
5
Nonnormal del Pezzo Surfaces
Miles
Reid
University of Warwick, COVENTRY, UNITED KINGDOM
This paper studies reduced, connected, Gorenstein surfaces with ample-K, assumed to be reducible or nonnormal. The normalisation is a union of one or more standard surfaces (scrolls and Veronese surfaces), marked with a conic as double locus. The question is how to glue these together to get a Gorenstein scheme. In characteristic 0, the results amount to a classification of projective surfaces in the style of the 1880s. However, the methods involve a study of the dualising sheaf of a nonnormal variety in terms of Rosenlicht differentials, and there is a subtle pathology in characteristic p due to Mori and S. Goto.
Commutative rings and algebras
General
695
727
10.2977/prims/1195165581
http://www.ems-ph.org/doi/10.2977/prims/1195165581
On H∞ Well-Posed Cauchy Problems for Some Weakly Hyperbolic Pseudo-differential Equations
Yasutoshi
Shiozaki
Kyoto University, KYOTO, JAPAN
Partial differential equations
General
729
743
10.2977/prims/1195165582
http://www.ems-ph.org/doi/10.2977/prims/1195165582
Division Theorems in Spaces of Entire Functions with Growth Conditions and their Applications to PDE of Infinite Order
Carlos
Berenstein
University of Maryland, COLLEGE PARK, UNITED STATES
Roger
Gay
Université de Bordeaux I, TALENCE CEDEX, FRANCE
Alekos
Vidras
University of Cyprus, NICOSIA, CYPRUS
It is shown that every entire function f ∈ Exp0(Cn), f(0) ≠ 0 is "slowly decreasing". As an application of this property, a theorem on analytic continuation of solutions of infinite order differential equations with constant coefficients is proven.
Several complex variables and analytic spaces
General
745
765
10.2977/prims/1195165583
http://www.ems-ph.org/doi/10.2977/prims/1195165583
Presentations of AF Algebras Associated to T-Graphs
David
Evans
University of Wales Cardiff, CARDIFF, UNITED KINGDOM
Jeremy
Gould
University of Wales Swansea, SWANSEA, UNITED KINGDOM
Functional analysis
General
767
798
10.2977/prims/1195165584
http://www.ems-ph.org/doi/10.2977/prims/1195165584
A von Neumann Algebra Framework for the Duality of the Quantum Groups
Tetsuya
Masuda
Kyoto University, KYOTO, JAPAN
Yoshiomi
Nakagami
Tokyo Institute of Technology, TOKYO, JAPAN
Functional analysis
General
799
850
10.2977/prims/1195165585
http://www.ems-ph.org/doi/10.2977/prims/1195165585
The Converse of Minlos' Theorem
Yoshiaki
Okazaki
Kyushu University, FUKUOKA, JAPAN
Yasuji
Takahashi
Yamaguchi University, YAMAGUCHI CITY, JAPAN
Probability theory and stochastic processes
General
851
863
10.2977/prims/1195165586
http://www.ems-ph.org/doi/10.2977/prims/1195165586
6
Action-angle Maps and Scattering Theory for Some Finite-dimensional Integrable Systems. II. Solitons, Antisolitons, and their Bound States
Simon
Ruijsenaars
Centre for Mathematics and Computer Science, AMSTERDAM, NETHERLANDS
We present an explicit construction of an action-angle map for the nonrelativistic Calogero-Moser systems with 1/sh2 and —1/ch2 pair potentials, and for relativistic generalizations thereof. The map is used to obtain extensive information concerning dynamics and scattering. We also discuss the relation between the relativistic N-particle systems and the N-particle-like solutions of various soliton PDEs, including the sine-Gordon equation.
Manifolds and cell complexes
General
865
1008
10.2977/prims/1195164945
http://www.ems-ph.org/doi/10.2977/prims/1195164945
Auslander Modules and Quasi-Homogeneity of Local Rings
Yuji
Yoshino
Kyoto University, KYOTO, JAPAN
Kiriko
Kato
Kyoto University, KYOTO, JAPAN
Commutative rings and algebras
General
1009
1038
10.2977/prims/1195164946
http://www.ems-ph.org/doi/10.2977/prims/1195164946
On the Admissibility of Singular Perturbations in Cauchy Problems II
Ryuichi
Ashino
Kyoto University, KYOTO, JAPAN
We shall give a new proof of the admissibility of singular perturbations, which was introduced by the author [2], without the assumption on the characteristic roots assumed in [2] using the method introduced by the author in [5, Appendix].
Partial differential equations
General
1039
1054
10.2977/prims/1195164947
http://www.ems-ph.org/doi/10.2977/prims/1195164947
Simply Typed Lambda Calculus with First-Class Environments
Shin-ya
Nishizaki
Okayama University, OKAYAMA, JAPAN
We propose a lambda calculus λ→env where it is possible to handle first-class environments. This calculus is based on the idea of explicit substitution, that is λ σ-calculus. Syntax of λ→env is obtained by merging the class of terms and the one of substitutions. Reduction is made from the weak reduction of λ σ-calculus. Its type system also originates in the one of λ σ-calculus. Confluence of λ→env is proved by Hardin's interpretation method which is originally used for proving confluence of λ σ-calculus. We proved strong normalizability of λ→env by reducing it to strong normalizability of a simply typed record calculus. Finally, we propose a type inference algorithm which produced a principal typing for each typable term.
Computer science
General
1055
1121
10.2977/prims/1195164948
http://www.ems-ph.org/doi/10.2977/prims/1195164948
On Unbounded Positive *-Representationson Fréchet-Domains
Wolf-Dieter
Heinrichs
Technische Universität Dresden, DRESDEN, GERMANY
Let D be a Fréchet-domain from Op*-algebra, abbreviated F-domain. The present paper is concerned with the study of positive *-representations of L+(D), of the Calkin representation of L+(D) and of bounded sets in ultrapower Du. For this the density property plays an important role. It was introduced by S. Heinrich for locally convex spaces in [2]. In the paper [3] we gave several characterizations of the density property of an F-domain D. In this work we give a characterizations of continuity of positive *-representations and Calkin representation of L+(D) by the density property of D. This generalizes the well-known result due to K. Schmiidgen, see [12], Further we describe bounded subsets in ultrapower Du. If D has the density property, then every bounded set M c Du has a simple structure: For each bounded set M c Du there exists a bounded set N c D with M c' Nu. S. Heinrich proved an analogous result for bounded ultrapowers on locally convex spaces.
Operator theory
General
1123
1138
10.2977/prims/1195164949
http://www.ems-ph.org/doi/10.2977/prims/1195164949
An Estimate of the Depth from an Intermediate Subfactor
Jerzy
Wierzbicki
Hokkaido University, SAPPORO, JAPAN
We show that for a triple K ⊂ N ⊂ M of type II1 factors the depth of the inclusion "K ⊂ M" is not greater than the maximum of depths of the inclusions "K ⊂ N" and "N ⊂ M" provided there is such a factor P, that the diagram P ⊂ M ∪ ∪ K ⊂ N is commuting and co-commuting square (or a non-degenerate commuting square) of type II1 factors.
General
1139
1144
10.2977/prims/1195164950
http://www.ems-ph.org/doi/10.2977/prims/1195164950