Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices

Details Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices

2005-01-14

arxiv.org/abs/math/0501219v1

Mathematics

Rings and Algebras

19 pages

Scientific paper

10.1016/j.aam.2005.03.007

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.

Affiliated with

Also associated with

No associations

Rating

Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$ Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-87992