TY - JOUR

T1 - Finitely presented algebras and groups defined by permutation relations

AU - Cedó, Ferran

AU - Jespers, Eric

AU - Okniński, Jan

PY - 2010/7/1

Y1 - 2010/7/1

N2 - The class of finitely presented algebras over a field K with a set of generators a1, ..., an and defined by homogeneous relations of the form a1 a2 ⋯ an = aσ (1) aσ (2) ⋯ aσ (n), where σ runs through a subset H of the symmetric group Symn of degree n, is introduced. The emphasis is on the case of a cyclic subgroup H of Symn of order n. A normal form of elements of the algebra is obtained. It is shown that the underlying monoid, defined by the same (monoid) presentation, has a group of fractions and this group is described. Properties of the algebra are derived. In particular, it follows that the algebra is a semiprimitive domain. Problems concerning the groups and algebras defined by arbitrary subgroups H of Symn are proposed. © 2009 Elsevier B.V. All rights reserved.

AB - The class of finitely presented algebras over a field K with a set of generators a1, ..., an and defined by homogeneous relations of the form a1 a2 ⋯ an = aσ (1) aσ (2) ⋯ aσ (n), where σ runs through a subset H of the symmetric group Symn of degree n, is introduced. The emphasis is on the case of a cyclic subgroup H of Symn of order n. A normal form of elements of the algebra is obtained. It is shown that the underlying monoid, defined by the same (monoid) presentation, has a group of fractions and this group is described. Properties of the algebra are derived. In particular, it follows that the algebra is a semiprimitive domain. Problems concerning the groups and algebras defined by arbitrary subgroups H of Symn are proposed. © 2009 Elsevier B.V. All rights reserved.

U2 - https://doi.org/10.1016/j.jpaa.2009.09.015

DO - https://doi.org/10.1016/j.jpaa.2009.09.015

M3 - Article

VL - 214

SP - 1095

EP - 1102

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

ER -