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The algebra of essential relations on a finite set

Bouc, Serge ; Thévenaz, Jacques

In: Journal für die reine und angewandte Mathematik (Crelles Journal), 2016, vol. 2016, no. 712, p. 225-250

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    Titre
    • The algebra of essential relations on a finite set
    Auteur
    • Bouc, Serge. CNRS-LAMFA, Université de Picardie - Jules Verne,33, rue St Leu, F-80039 Amiens Cedex 1, France
    • Thévenaz, Jacques. Section de mathématiques, EPFL,Station 8, CH-1015 Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal für die reine und angewandte Mathematik (Crelles Journal), 2016, vol. 2016, no. 712, p. 225-250. De Gruyter
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:326297
    Summary
    Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential relations. This quotient is called the essential algebra associated to X. We then define a suitable nilpotent ideal of the essential algebra and describe completely the structure of the corresponding quotient, a product of matrix algebras over suitable group algebras. In particular, we obtain a description of all the simple modules for the essential algebra.