### Abstract

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

pagine (da-a) | 550-566 |

Rivista | Journal of Algebra |

Volume | 275 |

Stato di pubblicazione | Published - 2004 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cita questo

*Journal of Algebra*,

*275*, 550-566.

**Gradings on the algebra of upper triangular matrices and their graded identities.** / Valenti, Angela; Di Vincenzo, Onofrio M.; Koshlukov, Plamen.

Risultato della ricerca: Article

*Journal of Algebra*, vol. 275, pagg. 550-566.

}

TY - JOUR

T1 - Gradings on the algebra of upper triangular matrices and their graded identities

AU - Valenti, Angela

AU - Di Vincenzo, Onofrio M.

AU - Koshlukov, Plamen

PY - 2004

Y1 - 2004

N2 - Let K be an infinite field and let UTn(K) denote the algebra of n x n upper triangular matrices over K. We describe all elementary gradings on this algebra. Further we describe the generators of the ideals of graded polynomial identities of UTn(K) and we produce linear bases of the corresponding relatively free graded algebras. We prove that one can distinguish the elementary gradings by their graded identities. We describe bases of the graded polynomial identities in several “typical” cases. Although in these cases we consider elementary gradings by cyclic groups, the same methods serve for elementary gradings by any finite group.

AB - Let K be an infinite field and let UTn(K) denote the algebra of n x n upper triangular matrices over K. We describe all elementary gradings on this algebra. Further we describe the generators of the ideals of graded polynomial identities of UTn(K) and we produce linear bases of the corresponding relatively free graded algebras. We prove that one can distinguish the elementary gradings by their graded identities. We describe bases of the graded polynomial identities in several “typical” cases. Although in these cases we consider elementary gradings by cyclic groups, the same methods serve for elementary gradings by any finite group.

UR - http://hdl.handle.net/10447/27733

M3 - Article

VL - 275

SP - 550

EP - 566

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -