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