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

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.

References in corpus (1)

• On the Graded Identities for Elementary Gradings in Matrix Algebras over Infinite Fields