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Invariants of semisimple Lie algebras acting on associative algebras

Author: Piotr Grzeszczuk
Journal: Proc. Amer. Math. Soc. 131 (2003), 709-717
MSC (2000): Primary 16W25; Secondary 16R20, 16U20
Published electronically: July 25, 2002
MathSciNet review: 1937407
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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.

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Additional Information

Piotr Grzeszczuk
Affiliation: Institute of Computer Science, Technical University of Białystok, Wiejska 45A, 15-351 Białystok, Poland

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
Article copyright: © Copyright 2002 American Mathematical Society

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