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

McConnell, J. C.

doi:10.1090/S0002-9939-1977-0453831-3

Representations of solvable Lie algebras. IV. An elementary proof of the $(U/P)_{E}$-structure theorem
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Proc. Amer. Math. Soc. 64 (1977), 8-12 Request permission

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

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Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Fasc. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). MR 0498737
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J. C. McConnell, Representations of solvable Lie algebras and the Gelfand-Kirillov conjecture, Proc. London Math. Soc. (3) 29 (1974), 453–484. MR 357529, DOI 10.1112/plms/s3-29.3.453
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 376791, DOI 10.24033/asens.1283

Dimension de Krull des algèbres de McConnell