Article
Licensed
Unlicensed
Requires Authentication
The algebra of essential relations on a finite set
-
Serge Bouc
and
Jacques Thévenaz
Published/Copyright:
April 3, 2014
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 all the simple modules for the essential algebra.
Received: 2013-10-29
Revised: 2014-2-26
Published Online: 2014-4-3
Published in Print: 2016-3-1
© 2016 by De Gruyter
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
