Graded Polynomial Identities for Matrices with the Transpose Involution over an Infinite Field

Abstract

Let $F$ be an infinite field, and let $M_n(F)$ be the algebra of $n\times n$ matrices over $F$. Suppose that this algebra is equipped with an elementary grading whose neutral component coincides with the main diagonal. In this paper, we find a basis for the graded polynomial identities of $M_n(F)$ with the transpose involution. Our results generalize for infinite fields of arbitrary characteristic previous results in the literature which were obtained for the field of complex numbers and for a particular class of elementary G-gradings.

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References in corpus (5)

• Representability and Specht problem for G-graded algebras
• Graded identities of block-triangular matrices
• On the Graded Identities for Elementary Gradings in Matrix Algebras over Infinite Fields
• Degree-inverting involutions on matrix algebras
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Cited by in corpus (1)

• Homogeneous involution on graded division algebras and their polynomial identities