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arXiv · 1006.3266

Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type

Ferran Cedo·Eric Jespers·Georg Klein
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Abstract

The class of finitely presented algebras over a field K with a set of generators a_1,...,a_n and defined by homogeneous relations of the form a_1a_2...a_n = a_{sigma(1)}a_{sigma(2)}...a_{sigma(n)}, where sigma runs through an abelian subgroup H of Sym_{n}, the symmetric group, is considered. It is proved that the Jacobson radical of such algebras is zero. Also, it is characterized when the monoid S_n(H), with the "same" presentation as the algebra, is cancellative in terms of the stabilizer of 1 and the stabilizer of n in H. This work is a continuation of earlier work of Cedo, Jespers and Okninski.

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Ferran Cedo, Eric Jespers, Georg Klein. 2010-06-16. Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type. https://doi.org/10.1016/j.jpaa.2011.10.021

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