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Proceedings of the American Mathematical Society

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Proof of the Gelfand-Kirillov conjecture for solvable Lie algebras


Author: A. Joseph
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0379617-3
Keywords: Gelfand-Kirillov conjecture, quotient field of Lie algebra, Weyl algebra
Article copyright: © Copyright 1974 American Mathematical Society

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