JournalsjcaVol. 4, No. 3pp. 215–267

The algebra of Boolean matrices, correspondence functors, and simplicity

  • Serge Bouc

    Université de Picardie-Jules Verne, Amiens, France

  • Jacques Thévenaz

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
The algebra of Boolean matrices, correspondence functors, and simplicity cover
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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 [3, 4], as well as some new ingredients in the theory of finite lattices.

Cite this article

Serge Bouc, Jacques Thévenaz, The algebra of Boolean matrices, correspondence functors, and simplicity. J. Comb. Algebra 4 (2020), no. 3, pp. 215–267

DOI 10.4171/JCA/44