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arXiv · 1701.08316

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

Luís Felipe Gonçalves Fonseca·Thiago Castilho de Mello
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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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Luís Felipe Gonçalves Fonseca, Thiago Castilho de Mello. 2017-01-28. Graded Polynomial Identities for Matrices with the Transpose Involution over an Infinite Field. https://doi.org/10.1080/00927872.2017.1350701

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