The trace algebra Cnd over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n, d 2. Starting with the generating set of C3d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C3d is equal to 7 for any d 3. We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8.
BENANTI, F.S., DRENSKY, V. (2007). Defining relations of minimal degree of the trace algebra of 3 X 3 matrices. COMPTES RENDUS DE L'ACADÉMIE BULGARE DES SCIENCES, 60(2), 103-110.
Defining relations of minimal degree of the trace algebra of 3 X 3 matrices
BENANTI, Francesca Saviella;
2007-01-01
Abstract
The trace algebra Cnd over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n, d 2. Starting with the generating set of C3d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C3d is equal to 7 for any d 3. We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8.
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