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Gel'fand‐Kirillov Conjecture on the Lie Field of an Algebraic Lie Algebra

### Abstract

This is an article written to review with sufficient detail the so‐called Gel'fand‐Kirillov conjecture concerning the isomorphisms between the quotient fields of the algebras generated by canonical variables [*p*_{i}, q_{j} ] = δ_{ ij }1 and the quotient fields of the universal enveloping algebras of algebraic Lie algebras. This conjecture sheds new light on the relation between the universal enveloping algebra of an algebraic Lie algebra and the Lie algebras of dynamic groups in quantum mechanics.

© 1969 The American Institute of Physics

Received 11 March 1968
Published online 04 November 2003

/content/aip/journal/jmp/10/6/10.1063/1.1664944

http://aip.metastore.ingenta.com/content/aip/journal/jmp/10/6/10.1063/1.1664944

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