## The algebra of essential relations on a finite set

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.

Published in:
Journal für die Reine und Angewandte Mathematik, 712, 225-250
Year:
2016
Publisher:
Walter de Gruyter
ISSN:
0075-4102
Laboratories: