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ACTIONS OF LIE SUPERALGEBRAS ON SEMIPRIME ALGEBRAS WITH CENTRAL INVARIANTS
Published online by Cambridge University Press: 24 June 2010
Abstract
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Let R be a semiprime algebra over a field 
of characteristic zero acted finitely on by a finite-dimensional Lie superalgebra L = L0 ⊕ L1. It is shown that if L is nilpotent, [L0, L1] = 0 and the subalgebra of invariants RL is central, then the action of L0 on R is trivial and R satisfies the standard polynomial identity of degree 2 ⋅ [
]. Examples of actions of nilpotent Lie superalgebras, with central invariants and with [L0, L1] ≠ 0, are constructed.
- Type
- Research Article
- Information
- Glasgow Mathematical Journal , Volume 52 , Issue A: Rings and Modules in Honour of Patrick F. Smith's 65th Birthday , July 2010 , pp. 93 - 102
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2010
References
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