Geodesic
The geometry of polynomial identities
Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 910-953

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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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     author = {C. Procesi},
     title = {The geometry of polynomial identities},
     journal = {Izvestiya. Mathematics },
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     number = {5},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_5_a5/}
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C. Procesi. The geometry of polynomial identities. Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 910-953. http://geodesic.mathdoc.fr/item/IM2_2016_80_5_a5/