<f>Z2</f>-graded cocharacters for superalgebras of triangular matrices

Let <f>K</f> be a field of characteristic zero, let <f>A</f>, <f>B</f> be <f>K</f>-algebras with polynomial identity and let <f>M</f> be a free <f>(A,B)</f>-bimodule. The algebra <f>R=<fen><cp type="lpar" style="s">A/0 M/B<cp type="rpar" style="s"></fen></f> can be endowed with a natural <f>Z2</f>-grading. In this paper, we compute the graded cocharacter sequence, the graded codimension sequence and the superexponent of <f>R</f>. As a consequence of these results, we also study the above PI-invariants in the setting of upper triangular matrices. In particular, we completely classify the algebra of <f>3×3</f> upper triangular matrices endowed with all possible <f>Z2</f>-gradings. [Copyright &y& Elsevier]