### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 756-782 |

Numero di pagine | 22 |

Rivista | Default journal |

Volume | 320 |

Stato di pubblicazione | Published - 2008 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cita questo

*Default journal*,

*320*, 756-782.

**Defining relations of minimal degree of the trace algebra of3 X 3 matrices.** / Benanti, Francesca Saviella; Drensky, Vesselin.

Risultato della ricerca: Article

*Default journal*, vol. 320, pagg. 756-782.

}

TY - JOUR

T1 - Defining relations of minimal degree of the trace algebra of3 X 3 matrices

AU - Benanti, Francesca Saviella

AU - Drensky, Vesselin

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - trace algebra

UR - http://hdl.handle.net/10447/40140

M3 - Article

VL - 320

SP - 756

EP - 782

JO - Default journal

JF - Default journal

ER -