On ℤn-graded identities of block-triangular matrices

The algebra of (Formula presented.) matrices over a field (Formula presented.) has a natural (Formula presented.) -grading. Its graded identities have been described by Vasilovsky who extended a previous work of Di Vincenzo for the algebra of (Formula presented.) matrices. In this paper, we study the graded identities of block-triangular matrices with the grading inherited by the grading of (Formula presented.). We show that its graded identities follow from the graded identities of (Formula presented.) and from its monomial identities of degree up to (Formula presented.). In the case of blocks of sizes (Formula presented.) and 1, we give a complete description of its monomial identities and exhibit a minimal basis for its (Formula presented.) -ideal