Abstract:
In this paper we stress the role of invariant theory and in particular the
role of varieties of semisimple representations in the theory of
polynomial identities of an associative algebra.
In particular, using this tool, we show that two
PI-equivalent finite-dimensional fundamental algebras
(see Definition 2.19) have the same semisimple part. Moreover, we carry
out some explicit computations of codimensions and cocharacters, extending
work of Berele [8] and Kanel-Belov [6], [7].
Keywords:polynomial identities, fundamental algebras, invariant theory.
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