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arXiv · 1407.1305

$2$-Graded Identities for the Tensor Square of the Grassmann Algebra

Diogo Diniz Pereira da Silva e Silva
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Abstract

We consider the algebra $E\otimes E$ over an infinite field equipped with a $\mathbb{Z}_2$-grading where the canonical basis is homogeneous and prove that in various cases the graded identites are just the ordinary ones. If the grading is a non-canonical grading obtained as a quotient grading of the natural $\mathbb{Z}_2\times\mathbb{Z}_2$-grading we exhibit a basis for the graded identities.

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Diogo Diniz Pereira da Silva e Silva. 2014-07-04. $2$-Graded Identities for the Tensor Square of the Grassmann Algebra. https://doi.org/10.1080/03081087.2014.896461

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