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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
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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  • [1] Walter Borho, Peter Gabriel, and Rudolf Rentschler, Primideale in Einhüllenden auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume), Lecture Notes in Mathematics, Vol. 357, Springer-Verlag, Berlin-New York, 1973 (German). MR 0376790
  • [2] Jacques Dixmier, Algèbres enveloppantes, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). Cahiers Scientifiques, Fasc. XXXVII. MR 0498737
  • [3] John C. McConnell and Moss Eisenberg Sweedler, Simplicity of smash products, Proc. London Math. Soc. (3) 23 (1971), 251–266. MR 0289607
  • [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
  • [5] J. C. McConnell, Representations of solvable Lie algebras. II. Twisted group rings, Ann. Sci. École Norm. Sup. (4) 8 (1975), no. 2, 157–178. MR 0376791
  • [6] P. Tauvel, Dimension de Krull des algèbres de McConnell, Univ. Pierre et Marie Curie, Paris VI (Preprint).

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Keywords: Completely solvable Lie algebra, universal enveloping algebra, ring of differential operators, Weyl algebra, twisted group ring
Article copyright: © Copyright 1977 American Mathematical Society