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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.


References [Enhancements On Off] (What's this?)

  • [1] W. Borho, P. Gabriel and R. Rentschler, Primideale in Einhüllenden auflösbarer Lie Algebren, Lecture Notes in Math., vol. 357, Springer-Verlag, Berlin and New York, 1973. MR 0376790 (51:12965)
  • [2] J. Dixmier, Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. MR 0498737 (58:16803a)
  • [3] J. C. McConnell and M. Sweedler, Simplicity of smash products, Proc. London Math. Soc. (3) 23 (1971), 251-266. MR 0289607 (44:6795)
  • [4] J. C. McConnell, Representations of solvable Lie algebras and the Gelfand-Kirillov conjecture, Proc. London Math. Soc. (3) 29 (1974), 453-484. MR 0357529 (50:9997)
  • [5] -, Representations of solvable Lie algebras. II: Twisted group rings, Ann. Sci. École Norm. Sup. (4) 8 (1975), 157-178. MR 0376791 (51:12966)
  • [6] P. Tauvel, Dimension de Krull des algèbres de McConnell, Univ. Pierre et Marie Curie, Paris VI (Preprint).

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Additional Information

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

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