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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Proof of the Gelfand-Kirillov conjecture for solvable Lie algebras
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by A. Joseph PDF
Proc. Amer. Math. Soc. 45 (1974), 1-10 Request permission

Abstract:

Let $g$ be a solvable algebraic Lie algebra over the complex numbers ${\mathbf {C}}$. It is shown that the quotient field of the enveloping algebra of $g$ is isomorphic to one of the standard fields ${D_{n,k}}$, being defined as the quotient field of the Weyl algebra of degree $n$ over ${\mathbf {C}}$ extended by $k$ indeterminates. This proves the Gelfand-Kirillov conjecture for $g$ solvable.
References
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 45 (1974), 1-10
  • MSC: Primary 17B35
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0379617-3
  • MathSciNet review: 0379617