### Abstract

The trace algebra Cnd over a field of characteristic 0 is generated by all tracesof products of d generic n × n matrices, n, d 2. Starting with the generating set ofC3d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degreeof the set of defining relations of C3d is equal to 7 for any d 3. We have determinedall relations of minimal degree. For d = 3 we have also found the defining relationsof degree 8.

Original language | English |
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Pages (from-to) | 103-110 |

Number of pages | 8 |

Journal | COMPTES RENDUS DE L'ACADÉMIE BULGARE DES SCIENCES |

Volume | 60 |

Publication status | Published - 2007 |

### All Science Journal Classification (ASJC) codes

- General

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## Cite this

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*, 103-110.