The algebra of Boolean matrices, correspondence functors, and simplicity
Representation Theory
2019-02-15 v1 Combinatorics
Category Theory
Group Theory
Rings and Algebras
Abstract
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence functor. The method uses the theory of such functors developed in [BT2, BT3], as well as some new ingredients in the theory of finite lattices.
Cite
@article{arxiv.1902.05422,
title = {The algebra of Boolean matrices, correspondence functors, and simplicity},
author = {Serge Bouc and Jacques Thévenaz},
journal= {arXiv preprint arXiv:1902.05422},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1510.03034