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Article Dans Une Revue Journal of Combinatorial Algebra Année : 2020

The algebra of Boolean matrices, correspondence functors, and simplicity

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Résumé

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.

Dates et versions

hal-03621750 , version 1 (28-03-2022)

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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⟩
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