Detecting Infinitely Many Semisimple Representations in a Fixed Finite Dimension
| dc.creator | Letzter, Edward S. | |
| dc.date | 2007-08-23 | |
| dc.date | 2008-07-20 | |
| dc.date.accessioned | 2026-07-07T09:51:10Z | |
| dc.date.available | 2026-07-07T09:51:10Z | |
| dc.description | Let $n$ be a positive integer, and let $k$ be a field (of arbitrary characteristic) accessible to symbolic computation. We describe an algorithmic test for determining whether or not a finitely presented $k$-algebra $R$ has infinitely many equivalence classes of semisimple representations $R \to M_n(k')$, where $k'$ is the algebraic closure of $k$. The test reduces the problem to computational commutative algebra over $k$, via famous results of Artin, Procesi, and Shirshov. The test is illustrated by explicit examples, with $n = 3$. | |
| dc.description | 12 pages, no figures. Revised; to appear in Journal of Algebra (Computational Section) | |
| dc.identifier | https://arxiv.org/abs/0708.3190 | |
| dc.identifier | http://arxiv.org/abs/0708.3190 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165195 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Commutative Algebra | |
| dc.subject | 16Z05 (Primary); 16R30, 13P10 (Secondary) | |
| dc.title | Detecting Infinitely Many Semisimple Representations in a Fixed Finite Dimension | |
| dc.type | text |