Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices
| dc.creator | Benanti, Francesca | |
| dc.creator | Drensky, Vesselin | |
| dc.date | 2005-01-14 | |
| dc.date.accessioned | 2026-07-07T06:29:40Z | |
| dc.date.available | 2026-07-07T06:29:40Z | |
| dc.description | The noncommutative (or mixed) trace algebra $T_{nd}$ is generated by $d$ generic $n\times n$ matrices and by the algebra $C_{nd}$ generated by all traces of products of generic matrices, $n,d\geq 2$. It is known that over a field of characteristic 0 this algebra is a finitely generated free module over a polynomial subalgebra $S$ of the center $C_{nd}$. For $n=3$ and $d=2$ we have found explicitly such a subalgebra $S$ and a set of free generators of the $S$-module $T_{32}$. We give also a set of defining relations of $T_{32}$ as an algebra and a Groebner basis of the corresponding ideal. The proofs are based on easy computer calculations with standard functions of Maple, the explicit presentation of $C_{32}$ in terms of generators and relations, and methods of representation theory of the general linear group. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0501219 | |
| dc.identifier | http://arxiv.org/abs/math/0501219 | |
| dc.identifier | doi:10.1016/j.aam.2005.03.007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98117 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16R30; 16S15 | |
| dc.title | Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices | |
| dc.type | text |