Invariants of semisimple Lie algebras acting on associative algebras

Grzeszczuk, Piotr

doi:10.1090/S0002-9939-02-06854-5

Invariants of semisimple Lie algebras acting on associative algebras
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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.

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