- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 11:02:59
4
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JNCG&vol=4&iss=1&update_since=2024-03-28
Journal of Noncommutative Geometry
J. Noncommut. Geom.
JNCG
1661-6952
1661-6960
Global analysis, analysis on manifolds
General
10.4171/JNCG
http://www.ems-ph.org/doi/10.4171/JNCG
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
4
2010
1
Quantum SO(3) groups and quantum group actions on M2
Piotr
Sołtan
University of Warsaw, WARSAW, POLAND
Quantum group, quantum group action, quantum family of maps
Answering a question of Shuzhou Wang we give a description of quantum SO(3) groups of Podleś as universal compact quantum groups acting on the C*-algebra M2 and preserving the Powers state. We use this result to give a complete classification of all continuous compact quantum group actions on M2.
Functional analysis
Associative rings and algebras
Nonassociative rings and algebras
Global analysis, analysis on manifolds
1
28
10.4171/JNCG/48
http://www.ems-ph.org/doi/10.4171/JNCG/48
Topological graph polynomials and quantum field theory Part I: heat kernel theories
Thomas
Krajewski
Aix-Marseille Université, CNRS Luminy, MARSEILLE CEDEX 9, FRANCE
Vincent
Rivasseau
Université Paris Sud-XI, ORSAY CEDEX, FRANCE
Adrian
Tanasă
Université de Bordeaux, TALENCE Cedex, FRANCE
Zhituo
Wang
Université Paris Sud-XI, ORSAY CEDEX, FRANCE
Parametric representation in (non)commutative field theory, Tutte polynomial, Bollobás–Riordan polynomial
We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first article we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial, and how the new polynomials of noncommutative quantum field theory are special versions of the Bollobás–Riordan polynomials.
Quantum theory
Combinatorics
General
29
82
10.4171/JNCG/49
http://www.ems-ph.org/doi/10.4171/JNCG/49
Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture
Ronghui
Ji
Indiana University Purdue University Indianapolis, INDIANAPOLIS, UNITED STATES
Crichton
Ogle
Ohio State University, COLUMBUS, UNITED STATES
Bobby
Ramsey
University of Hawai‘i at Mānoa, HONOLULU, UNITED STATES
ℬ-bounded cohomology, rapid decay algebras, Bass conjecture
By deploying dense subalgebras of ℓ1(G) we generalize the Bass conjecture in terms of Connes’ cyclic homology theory. In particular, we propose a stronger version of the ℓ1-Bass Conjecture. We prove that hyperbolic groups relative to finitely many subgroups, each of which posses the polynomial conjugacy bound property and nilpotent periodicity property, satisfy the ℓ1-Stronger-Bass Conjecture. Moreover, we determine the conjugacy bound for relatively hyperbolic groups and compute the cyclic cohomology of the ℓ1-algebra of any discrete group.
Functional analysis
Associative rings and algebras
Group theory and generalizations
General
83
124
10.4171/JNCG/50
http://www.ems-ph.org/doi/10.4171/JNCG/50
A Lefschetz fixed-point formula for certain orbifold C*-algebras
Siegfried
Echterhoff
Universität Münster, MÜNSTER, GERMANY
Heath
Emerson
University of Victoria, VICTORIA, B.C., CANADA
Hyun Jeong
Kim
University of Victoria, VICTORIA, B.C., CANADA
Lefschetz fixed point theorem, K-theory, KK-theory, noncommutative geometry, orbifolds
Using Poincaré duality in K-theory, we state and prove a Lefschetz fixed point formula for endomorphisms of crossed product C*-algebras C0(X) ⋊ G coming from covariant pairs. Here G is assumed countable, X a manifold, and X ⋊ G cocompact and proper. The formula in question describes the graded trace of the map induced by the automorphism on K-theory of C0(X) ⋊ G, i.e. the Lefschetz number, in terms of fixed orbits of the spatial map. Each fixed orbit contributes to the Lefschetz number by a formula involving twisted conjugacy classes of the corresponding isotropy group, and a secondary construction that associates, by way of index theory, a group character to any finite group action on a Euclidean space commuting with a given invertible matrix.
$K$-theory
Functional analysis
General
125
155
10.4171/JNCG/51
http://www.ems-ph.org/doi/10.4171/JNCG/51