The algebra of Boolean matrices, correspondence functors, and simplicity

Serge Bouc (1) , Jacques Thevenaz

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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 [3, 4], as well as some new ingredients in the theory of finite lattices.

Domaines: Mathématiques [math]

Serge Bouc, Jacques Thevenaz. The algebra of Boolean matrices, correspondence functors, and simplicity. Journal of Combinatorial Algebra, 2020, 4 (3), pp.215-267. ⟨10.4171/JCA/44⟩. ⟨hal-03621750⟩