Graded central polynomials for the matrix algebra of order two

Daniela La Mattina, Antônio Pereira Brandão Jr., Plamen Koshlukov, Alexei Krasilnikov

Risultato della ricerca: Other contribution

5 Citazioni (Scopus)

Abstract

Let K be an infinite integral domain and $A=M_2(K)$ the algebraof $2\times 2$ matrices over $K$. The authors consider thenatural $\mathbb{Z}_2$-grading of $A$ obtained by requiring thatthe diagonal matrices and the off-diagonal matricesare of homogeneous degree $0$ and $1$, respectively.When $K$ is a field, a basis of the graded identities of $A$ wasdescribed in [O. M. Di Vincenzo, On the graded identities of$M_{1,1}(E).$ Israel J. Math. 80 (1992), no. 3, 323-–335] in case$\mbox{char}\, K = 0$ and in [P. E. Koshlukov and S. S. de Azevedo,Graded identities for T-prime algebras over fields of positivecharacteristic. Israel J. Math. 128 (2002), 157-–176] when $K$ isinfinite and $\mbox{char}\, K >2$.Here the authors remark that the same basis holds in case K is aninfinite integral domain.They also study the $T_2$-space of central polynomials of$A$ and find a finite set of generators. Their proofdoes not depend on the characteristic, hence holds also forinfinite fields of characteristic $2.$
Lingua originaleEnglish
Stato di pubblicazionePublished - 2009

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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La Mattina, D., Brandão Jr., A. P., Koshlukov, P., & Krasilnikov, A. (2009). Graded central polynomials for the matrix algebra of order two.