Fixed algebras of residually nilpotent Lie algebras

Author:
Vesselin Drensky

Journal:
Proc. Amer. Math. Soc. **120** (1994), 1021-1028

MSC:
Primary 17B40

DOI:
https://doi.org/10.1090/S0002-9939-1994-1181161-3

MathSciNet review:
1181161

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Abstract: Let be the free Lie algebra of rank over a field , and let be an ideal of such that and the algebra is residually nilpotent. Let be a finite group of automorphisms of and the order of be invertible in . We establish that the algebra of fixed points is not finitely generated. The class of algebras under consideration contains the free Lie algebra over an arbitrary field and the relatively free algebras in nonnilpotent varieties of Lie algebras over infinite fields of characteristic different from and .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1181161-3

Keywords:
Fixed points of automorphisms of Lie algebras,
residually nilpotent Lie algebras,
free Lie algebras

Article copyright:
© Copyright 1994
American Mathematical Society