%0 Journal Article %T The algebra of Boolean matrices, correspondence functors, and simplicity %+ Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA) %A Bouc, Serge %A Thevenaz, Jacques %< avec comité de lecture %@ 2415-6302 %J Journal of Combinatorial Algebra %I European Mathematical Society Press %V 4 %N 3 %P 215-267 %8 2020 %D 2020 %Z 1902.05422 %R 10.4171/JCA/44 %Z Mathematics [math]Journal articles %X 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. %G English %L hal-03621750 %U https://u-picardie.hal.science/hal-03621750 %~ CNRS %~ UNIV-PICARDIE %~ INSMI %~ U-PICARDIE %~ LAMFA