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 -