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arXiv · 1310.7695

The algebra of essential relations on a finite set

Serge Bouc·Jacques Thévenaz
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Abstract

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 the Jacobson radical and of all the simple modules for the essential algebra.

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Serge Bouc, Jacques Thévenaz. 2013-10-29. The algebra of essential relations on a finite set. https://arxiv.org/abs/1310.7695

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