TY - JOUR

T1 - Finitely presented monoids and algebras defined by permutation relations of abelian type

AU - Cedó, Ferran

AU - Jespers, Eric

AU - Klein, Georg

PY - 2012/5/1

Y1 - 2012/5/1

N2 - 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 σ(1)a σ(2)⋯a σ(n), where σ 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, can be embedded in a group in terms of the stabilizer of 1 and the stabilizer of n in H, where H is an arbitrary subgroup of Sym n. This work is a continuation of earlier work of Cedó, Jespers and Okniński. © 2011 Elsevier B.V.

AB - 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 σ(1)a σ(2)⋯a σ(n), where σ 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, can be embedded in a group in terms of the stabilizer of 1 and the stabilizer of n in H, where H is an arbitrary subgroup of Sym n. This work is a continuation of earlier work of Cedó, Jespers and Okniński. © 2011 Elsevier B.V.

U2 - https://doi.org/10.1016/j.jpaa.2011.10.021

DO - https://doi.org/10.1016/j.jpaa.2011.10.021

M3 - Article

VL - 216

SP - 1033

EP - 1039

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

ER -