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Abstract
The algebra of matrices over a field
has a natural
-grading. Its graded identities have been described by Vasilovsky who extended a previous work of Di Vincenzo for the algebra of
matrices. In this paper, we study the graded identities of block-triangular matrices with the grading inherited by the grading of
. We show that its graded identities follow from the graded identities of
and from its monomial identities of degree up to
. In the case of blocks of sizes
and 1, we give a complete description of its monomial identities and exhibit a minimal basis for its
-ideal.
Notes
T. C. de Mello is supported by the FAPESP [grant number 2012/16838-0].