The geometry of polynomial identities

C. Procesi

Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 910-953.

Résumé

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].

Détail

Mots-clés : polynomial identities, fundamental algebras, invariant theory.

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