Finitely presented algebras and groups defined by permutation relations

dc.creatorCedo, F.
dc.creatorJespers, E.
dc.creatorOkninksi, J.
dc.date2008-10-02
dc.date.accessioned2026-07-07T10:07:02Z
dc.date.available2026-07-07T10:07:02Z
dc.descriptionThe 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 $a_{1}a_{2}... a_{n} =a_{σ(a)} a_{σ(2)} ... a_{σ(n)}$, where $σ$ runs through a subset $H$ of the symmetric group $\Sym_{n}$ of degree $n$, is introduced. The emphasis is on the case of a cyclic subgroup $H$ of $\Sym_{n}$ 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 $\Sym_{n}$ are proposed.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0810.0352
dc.identifierhttp://arxiv.org/abs/0810.0352
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170497
dc.subjectRings and Algebras
dc.subject16S15; 16S36; 20F05; 20M05
dc.titleFinitely presented algebras and groups defined by permutation relations
dc.typetext

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