Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Defining Relations of Noncommutative Trace Algebra of Two $3 \times 3$
  Matrices   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.

19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: stat