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

Angela Valenti, Onofrio M. Di Vincenzo, Plamen Koshlukov

Risultato della ricerca: Article

31 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
pagine (da-a)550-566
RivistaJournal of Algebra
Volume275
Stato di pubblicazionePublished - 2004

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Upper triangular matrix
Grading
Algebra
Polynomial Identities
Free Algebras
Graded Algebra
Cyclic group
Triangular
Finite Group
Generator
Denote

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cita questo

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

In: Journal of Algebra, Vol. 275, 2004, pag. 550-566.

Risultato della ricerca: Article

Valenti, A, Di Vincenzo, OM & Koshlukov, P 2004, 'Gradings on the algebra of upper triangular matrices and their graded identities', Journal of Algebra, vol. 275, pagg. 550-566.
Valenti A, Di Vincenzo OM, Koshlukov P. Gradings on the algebra of upper triangular matrices and their graded identities. Journal of Algebra. 2004;275:550-566.
Valenti, Angela ; Di Vincenzo, Onofrio M. ; Koshlukov, Plamen. / Gradings on the algebra of upper triangular matrices and their graded identities. In: Journal of Algebra. 2004 ; Vol. 275. pagg. 550-566.
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