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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invariants of semisimple Lie algebras acting on associative algebras
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by Piotr Grzeszczuk PDF
Proc. Amer. Math. Soc. 131 (2003), 709-717 Request permission

Abstract:

If ${\mathfrak g}$ is a Lie algebra of derivations of an associative algebra $R$, then the subalgebra of invariants is the set $R^{\mathfrak g} = \{ r \in R \mid \delta (r) = 0 \ \text { for all } \delta \in {\mathfrak g}\}.$ In this paper, we study the relationship between the structure of $R^{\mathfrak g}$ and the structure of $R$, where $\mathfrak g$ is a finite dimensional semisimple Lie algebra over a field of characteristic zero acting finitely on $R$, when $R$ is semiprime.
References
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Additional Information
  • Piotr Grzeszczuk
  • Affiliation: Institute of Computer Science, Technical University of Białystok, Wiejska 45A, 15-351 Białystok, Poland
  • Email: piotrgr@cksr.ac.bialystok.pl
  • Received by editor(s): October 19, 2001
  • Published electronically: July 25, 2002
  • Additional Notes: The author was supported by Polish scientific grant KBN no. 2 P03A 039 14.
  • Communicated by: Martin Lorenz
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 709-717
  • MSC (2000): Primary 16W25; Secondary 16R20, 16U20
  • DOI: https://doi.org/10.1090/S0002-9939-02-06854-5
  • MathSciNet review: 1937407