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Proceedings of the American Mathematical Society

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Representations of solvable Lie algebras. IV. An elementary proof of the $ (U/P)\sb{E}$-structure theorem


Author: J. C. McConnell
Journal: Proc. Amer. Math. Soc. 64 (1977), 8-12
MSC: Primary 17B30
DOI: https://doi.org/10.1090/S0002-9939-1977-0453831-3
MathSciNet review: 0453831
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Abstract: In this paper we give a shorter and much more elementary proof of a theorem which describes the structure of certain localisations of the enveloping algebra of a completely solvable Lie algebra. Such a localisation is shown to be a twisted group algebra where the group is free abelian of finite rank and the coefficient ring is a polynomial extension of a Weyl algebra.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0453831-3
Keywords: Completely solvable Lie algebra, universal enveloping algebra, ring of differential operators, Weyl algebra, twisted group ring
Article copyright: © Copyright 1977 American Mathematical Society