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