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

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.

15 pages

Cited by in corpus (5)

• Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type, II
• Construction of a two unique product semigroup defined by permutation relations of quaternion type
• Finitely presented algebras defined by permutation relations of dihedral type
• Gröbner-Shirshov basis for the finitely presented algebras defined by permutation relations of symmetric type
• Group algebras and semigroup algebras defined by permutation relations of fixed length