Title | **Defining relations of the noncommutative trace algebra of two matrices** |

Author(s) | Francesca Benanti, Vesselin Drensky |

Type | Article in Journal |

Abstract | The noncommutative (or mixed) trace algebra T n d is generated by d generic n × n matrices and by the algebra C n d generated by all traces of products of generic matrices, n , d ⩾ 2 . It is known that over a field of characteristic 0 this algebra is a finitely generated free module over a polynomial subalgebra S of the center C n d . For n = 3 and d = 2 we have found explicitly such a subalgebra S and a set of free generators of the S-module T 32 . We give also a set of defining relations of T 32 as an algebra and a Gröbner basis of the corresponding ideal. The proofs are based on easy computer calculations with standard functions of Maple, the explicit presentation of C 32 in terms of generators and relations, and methods of representation theory of the general linear group. |

Keywords | Generic matrices, Matrix invariants and concomitants, Trace algebras, Defining relations, Gröbner basis |

ISSN | 0196-8858 |

URL |
http://www.sciencedirect.com/science/article/pii/S0196885806000431 |

Language | English |

Journal | Advances in Applied Mathematics |

Volume | 37 |

Number | 2 |

Pages | 162 - 182 |

Year | 2006 |

Note | Special issue in honor of Amitai Regev on his 65th birthday |

Edition | 0 |

Translation |
No |

Refereed |
No |