Central invariants of Lie color algebras acting on group-graded algebras
by
Malgorzata Hryniewicka
University of Bialystok
Coauthors: Piotr Grzeszczuk (University of Bialystok)

There have been many papers analyzing the invariants of actions of Lie algebras on associative algebras. In [BG] Jeffrey Bergen and Piotr Grzeszczuk show that if R is a semiprime K-algebra acted on by a finite-dimensional nilpotent Lie algebra L of algebraic derivations and if the subalgebra of invariants R^L is central, then R satisfies a polynomial identity. Lie algebras can be considered as part of a larger class of nonassociative algebras known as Lie color algebras. Our aim is to extend this result to the actions of Lie color algebras on semiprime algebras graded by finite abelian groups.

References

[BG] Jeffrey Bergen and Piotr Grzeszczuk, Invariants of Lie superalgebras acting on associative algebras, Israel J. Math. 94 (1996), 403-428.

Date received: June 29, 2000