Finitely presented algebras and groups defined by permutation relations
| dc.creator | Cedo, F. | |
| dc.creator | Jespers, E. | |
| dc.creator | Okninksi, J. | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:07:02Z | |
| dc.date.available | 2026-07-07T10:07:02Z | |
| dc.description | 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 $a_{1}a_{2}... a_{n} =a_{σ(a)} a_{σ(2)} ... a_{σ(n)}$, 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.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0810.0352 | |
| dc.identifier | http://arxiv.org/abs/0810.0352 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170497 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16S15; 16S36; 20F05; 20M05 | |
| dc.title | Finitely presented algebras and groups defined by permutation relations | |
| dc.type | text |