### Abstract

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.

Lingua originale | English |
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pagine (da-a) | 756-782 |

Numero di pagine | 22 |

Rivista | Journal of Algebra |

Volume | 320 |

Stato di pubblicazione | Published - 2008 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cita questo

Benanti, F. S., & Drensky, V. (2008). Defining relations of minimal degree of the trace algebra of3 X 3 matrices.

*Journal of Algebra*,*320*, 756-782.