Group-theoretical graph categories
Quantum Algebra
2022-03-25 v2 Combinatorics
Abstract
The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of partitions (more general; due to Maassen, 2018). We generalize these results to the case of graph categories, which allows to replace the symmetric group by the group of automorphisms of some graph.
Cite
@article{arxiv.2009.06998,
title = {Group-theoretical graph categories},
author = {Daniel Gromada},
journal= {arXiv preprint arXiv:2009.06998},
year = {2022}
}
Comments
32 pages; changes: removed former Section 4.4 (as superfluous), modified formulation of Thm. B, made some additional minor changes and corrections