Displaying similar documents to “ k + l × 2 -graded polynomial identities for M k , l ( E ) E

A Basis for Z-Graded Identities of Matrices over Infinite Fields

Azevedo, Sergio (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 16R10, 16R20, 16R50 The algebra Mn(K) of the matrices n × n over a field K can be regarded as a Z-graded algebra. In this paper, it is proved that if K is an infinite field, all the Z-graded polynomial identities of Mn(K) follow from the identities: x = 0, |α(x)| ≥ n, xy = yx, α(x) = α(y) = 0, xyz = zyx, α(x) = −α(y) = α(z ), where α is the degree of the corresponding variable. This is a generalization of a result of Vasilovsky about...

Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices

Di Vincenzo, Onofrio (2004)

Serdica Mathematical Journal

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000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55. We present some results about the Z2-graded polynomial identities of block-triangular matrix superalgebras R[[A M],[0 B]]. In particular, we describe conditions for the T2-ideal of a such superalgebra to be factorable as the product T2(A)T2(B). Moreover, we give formulas for computing the sequence of the graded cocharacters of R in some interesting case. Partially supported by MURST COFIN...

On Ordinary and Z2-graded Polynomial Identities of the Grassmann Algebra

Ribeiro Tomaz da Silva, Viviane (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary: 16R10, Secondary: 16W55. The main purpose of this paper is to provide a survey of results concerning the ordinary and Z2-graded polynomial identities of the infinite dimensional Grassmann algebra over a field of characteristic zero, as well as of its sequences of ordinary and Z2-graded codimensions and cocharacters. We also intend to describe briefly the techniques used by the authors in order to illustrate some important...

Gradings and Graded Identities for the Matrix Algebra of Order Two in Characteristic 2

Koshlukov, Plamen, César dos Reis, Júlio (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R10, 16R99, 16W50. Let K be an infinite field and let M2(K) be the matrix algebra of order two over K. The polynomial identities of M2(K) are known whenever the characteristic of K is different from 2. The algebra M2(K) admits a natural grading by the cyclic group of order 2; the graded identities for this grading are known as well. But M2(K) admits other gradings that depend on the field and on its characteristic. Here we describe...

On some recent results about the graded Gelfand-Kirillov dimension of graded PI-algebras

Centrone, Lucio (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R10, 16W55, 15A75. We survey some recent results on graded Gelfand-Kirillov dimension of PI-algebras over a field F of characteristic 0. In particular, we focus on verbally prime algebras with the grading inherited by that of Vasilovsky and upper triangular matrices, i.e., UTn(F), UTn(E) and UTa,b(E), where E is the infinite dimensional Grassmann algebra.

A Basis for the Graded Identities of the Pair (M2(K), gl2(K))

Koshlukov, Plamen, Krasilnikov, Alexei (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R10, 17B01. Let M2(K) be the algebra of 2×2 matrices over an infinite integral domain K. In this note we describe a basis for the Z2-graded identities of the pair (M2(K),gl2(K)). ∗ Partially supported by CNPq (Grant 304003/2011-5) and FAPESP (Grant 2010/50347-9). ∗∗ Partially supported by CNPq, DPP/UnB and by CNPq-FAPDF PRONEX grant 2009/00091-0 (193.000.580/2009).