The trace algebra Cnd over a field of characteristic 0 is generatedby all traces of products of d generic n × n matrices, n, d 2. Minimal setsof generators of Cnd are known for n = 2 and n = 3 for any d as well as forn = 4 and n = 5 and d = 2. The defining relations between the generatorsare found for n = 2 and any d and for n = 3, d = 2 only. Starting withthe generating set of C3d given by Abeasis and Pittaluga in 1989, we haveshown that the minimal degree of the set of defining relations of C3d is equalto 7 for any d 3. We have determined all relations of minimal degree. Ford = 3 we have also found the defining relations of degree 8. The proofs arebased on methods of representation theory of the general linear group and easycomputer calculations with standard functions of Maple.
|Numero di pagine||22|
|Rivista||Journal of Algebra|
|Stato di pubblicazione||Published - 2008|
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