English

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.

Keywords

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

R2 v1 2026-06-23T07:41:06.262Z