- journal articles metadata
European Mathematical Society Publishing House
2024-03-19 07:55:06
4
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JCA&vol=2&iss=1&update_since=2024-03-19
Journal of Combinatorial Algebra
J. Comb. Algebra
JCA
2415-6302
2415-6310
Combinatorics
Group theory and generalizations
10.4171/JCA
http://www.ems-ph.org/doi/10.4171/JCA
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
2
2018
1
On joins and intersections of subgroups in free groups
Sergei
Ivanov
University of Illinois, Urbana, USA
Free groups, Stallings graphs, intersections and joins of subgroups
We study graphs of (generalized) joins and intersections of finitely generated subgroups of a free group. We show how to disprove a lemma of Imrich and Müller on these graphs, how to repair the lemma and how to utilize it.
Group theory and generalizations
Manifolds and cell complexes
1
18
10.4171/JCA/2-1-1
http://www.ems-ph.org/doi/10.4171/JCA/2-1-1
2
8
2018
The periplectic Brauer algebra II: Decomposition multiplicities
Kevin
Coulembier
University of Sydney, Australia
Michael
Ehrig
University of Sydney, Australia
Periplectic Lie superalgebra, periplectic Brauer algebra, decomposition multiplicities, (skew) Young diagrams, standardly based algebras
We determine the Jordan–Hölder decomposition multiplicities of projective and cell modules over periplectic Brauer algebras in characteristic zero. These are obtained by developing the combinatorics of certain skew Young diagrams.We also establish a useful relationship with the Kazhdan–Lusztig multiplicities of the periplectic Lie supergroup.
Associative rings and algebras
Nonassociative rings and algebras
Quantum theory
19
46
10.4171/JCA/2-1-2
http://www.ems-ph.org/doi/10.4171/JCA/2-1-2
2
8
2018
On skew braces (with an appendix by N. Byott and L. Vendramin)
Agata
Smoktunowicz
University of Edinburgh, UK
Leandro
Vendramin
University of Buenos Aires, Argentina
Braces, Yang–Baxter, rings, near-rings, triply factorized groups, matched pair of groups, bijective 1-cocycles, Hopf–Galois extensions
Braces are generalizations of radical rings, introduced by Rump to study involutive non-degenerate set-theoretical solutions of the Yang–Baxter equation (YBE). Skew braces were also recently introduced as a tool to study not necessarily involutive solutions. Roughly speaking, skew braces provide group-theoretical and ring-theoretical methods to understand solutions of the YBE. It turns out that skew braces appear in many different contexts, such as near-rings, matched pairs of groups, triply factorized groups, bijective 1-cocycles and Hopf–Galois extensions. These connections and some of their consequences are explored in this paper. We produce several new families of solutions related in many different ways with rings, near-rings and groups. We also study the solutions of the YBE that skew braces naturally produce. We prove, for example, that the order of the canonical solution associated with a finite skew brace is even: it is two times the exponent of the additive group modulo its center.
Associative rings and algebras
Quantum theory
47
86
10.4171/JCA/2-1-3
http://www.ems-ph.org/doi/10.4171/JCA/2-1-3
2
8
2018
Remarks on profinite groups having few open subgroups
Dan
Segal
Oxford University, UK
Profinite groups, strong completeness
We explore the relations between various conditions of „smallness" on profinite groups.
Group theory and generalizations
87
101
10.4171/JCA/2-1-4
http://www.ems-ph.org/doi/10.4171/JCA/2-1-4
2
8
2018