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Abstract
Let A be a superalgebra over a field of characteristic zero. In this paper we investigate the graded polynomial identities of A through the asymptotic behavior of a numerical sequence called the sequence of graded codimensions of A. Our main result says that such sequence is polynomially bounded if and only if the variety of superalgebras generated by A does not contain a list of five superalgebras consisting of a 2-dimensional algebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and nontrivial gradings. Our main tool is the representation theory of the symmetric group.
ACKNOWLEDGMENT
The first author was partially supported by MURST of Italy; the second author was partially supported by RBRF, grants 98-01-01020 and 99-01-00233, the third author was partially supported by RBRF, grants 99-01-00233 and 00-15-96128.