JJ-trace identities and invariant theory

We generalize the notion of trace identity to $J$-trace. Our main result is that all $J$-traces of $M_{n,n}$ are consequence of those of degree $\frac12n(n + 3)$. This also gives an indirect description of the queer trace identities of $M_n(E)$

Computing Super Matrix Invariants

In [Trace identities and $\bf {Z}/2\bf {Z}$-graded invariants, {\it Trans. Amer. Math. Soc. \bf309} (1988), 581--589] we generalized the first and second fundamental theorems of invariant theory from the general linear group to the general linear Lie superalgebra. In the current paper we generalize the computations of the the numerical invariants (multiplicities and Poincar\'e series) to the superalgebra case. The results involve either inner products of symmetric functions in two sets of variables, or complex integrals. we generalized the first and second fundamental theorems of invariant theory from the general linear group to the general linear Lie superalgebra. In the current paper we generalize the computations of the the numerical invariants (multiplicities and Poincar\'e series) to the superalgebra case. The results involve either inner products of symmetric functions in two sets of variables, or complex integrals

Some Questions about products of verbally prime T-ideals

2010 Mathematics Subject Classification: 16R10.In [1] we studied identities of finite dimensional incidence algebras and showed how they were gotten by products and intersections of identities of matrices and we left open the question of when two incidence algebras satisfy the same identities, a problem which is still open. In the current paper we re-visit this problem: We describe it, give some partial results and some related problems based on the work of Kemer.* Support by DePaul University Faculty Research Council gratefully acknowledged