### Abstract

Original language | English |
---|---|

Publication status | Published - 2009 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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

Research output: Other contribution

*Graded central polynomials for the matrix algebra of order two*..

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TY - GEN

T1 - Graded central polynomials for the matrix algebra of order two

AU - La Mattina, Daniela

AU - Koshlukov, Plamen

AU - Krasilnikov, Alexei

AU - Brandão Jr., Antônio Pereira

PY - 2009

Y1 - 2009

N2 - Let K be an infinite integral domain and $A=M_2(K)$ the algebra of $2\times 2$ matrices over $K$. The authors consider the natural $\mathbb{Z}_2$-grading of $A$ obtained by requiring that the diagonal matrices and the off-diagonal matrices are of homogeneous degree $0$ and $1$, respectively. When $K$ is a field, a basis of the graded identities of $A$ was described 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 positive characteristic. Israel J. Math. 128 (2002), 157-–176] when $K$ is infinite and $\mbox{char}\, K >2$. Here the authors remark that the same basis holds in case K is an infinite integral domain. They also study the $T_2$-space of central polynomials of $A$ and find a finite set of generators. Their proof does not depend on the characteristic, hence holds also for infinite fields of characteristic $2.$

AB - Let K be an infinite integral domain and $A=M_2(K)$ the algebra of $2\times 2$ matrices over $K$. The authors consider the natural $\mathbb{Z}_2$-grading of $A$ obtained by requiring that the diagonal matrices and the off-diagonal matrices are of homogeneous degree $0$ and $1$, respectively. When $K$ is a field, a basis of the graded identities of $A$ was described 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 positive characteristic. Israel J. Math. 128 (2002), 157-–176] when $K$ is infinite and $\mbox{char}\, K >2$. Here the authors remark that the same basis holds in case K is an infinite integral domain. They also study the $T_2$-space of central polynomials of $A$ and find a finite set of generators. Their proof does not depend on the characteristic, hence holds also for infinite fields of characteristic $2.$

KW - central polynomials

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

UR - http://www.ams.org/mathscinet/pdf/2520727.pdf?pg1=RVRI&pg3=authreviews&s1=734661&vfpref=html&r=4

M3 - Other contribution

ER -