TY - GEN

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

AU - La Mattina, Daniela

AU - Brandão Jr., Antônio Pereira

AU - Koshlukov, Plamen

AU - Krasilnikov, Alexei

PY - 2009

Y1 - 2009

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

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 -