A presentation of the trace algebra of three 3x3 matrices

Details A presentation of the trace algebra of three 3x3 matrices A presentation of the trace algebra of three 3x3 matrices

2011-04-05

arxiv.org/abs/1104.0904v1

Mathematics

Rings and Algebras

Scientific paper

The trace algebra C_{nd} is generated by all traces of products of d generic n x n matrices. Minimal generating sets of C_{nd} and their defining relations are known for n < 3 and n = 3, d=2. This paper states a minimal generating set and their defining relations for n=d=3. Furthermore the computations yield a description of C_{33} as a free module over the ring generated by a homogeneous system of parameters.

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