# 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 originale English Published - 2009

Matrix Algebra
Integral domain
Polynomial
Diagonal matrix
Finite Set
Generator
Algebra

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### Cita questo

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

Graded central polynomials for the matrix algebra of order two. / La Mattina, Daniela; Brandão Jr., Antônio Pereira; Koshlukov, Plamen; Krasilnikov, Alexei.

2009, .

Risultato della ricerca: Other contribution

La Mattina, D, Brandão Jr., AP, Koshlukov, P & Krasilnikov, A 2009, Graded central polynomials for the matrix algebra of order two..
La Mattina D, Brandão Jr. AP, Koshlukov P, Krasilnikov A. Graded central polynomials for the matrix algebra of order two. 2009.
La Mattina, Daniela ; Brandão Jr., Antônio Pereira ; Koshlukov, Plamen ; Krasilnikov, Alexei. / Graded central polynomials for the matrix algebra of order two. 2009.
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N2 - 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 $2.$

AB - 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 $2.$

KW - central polynomials

UR - http://hdl.handle.net/10447/75679

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M3 - Other contribution

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