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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 5, Pages 103–152 (Mi izv8436)  

The geometry of polynomial identities

C. Procesi

Mathematics Department, University of Rome "La Sapienza", Italy

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.

DOI: https://doi.org/10.4213/im8436

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English version:
Izvestiya: Mathematics, 2016, 80:5, 910–953

Bibliographic databases:

Document Type: Article
UDC: 512.552.4+512.547.212
MSC: 15A24, 16R10, 16R30
Received: 01.08.2015

Citation: C. Procesi, “The geometry of polynomial identities”, Izv. RAN. Ser. Mat., 80:5 (2016), 103–152; Izv. Math., 80:5 (2016), 910–953

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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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