2-Graded identities for the tensor square of the Grassmann algebra

Abstract

We consider the algebra over an infinite field equipped with a -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 -graded, we exhibit a basis for the graded identities.

Keywords:

• graded algebras
• graded polynomial identities
• grassmann algebra

AMS Subject Classifications:

• 16W50
• 16R10
• 15A75

Acknowledgements

We thank CNPq for the finantial support and the referee for valuable remarks.