Gel'fand-Kirillov Conjecture on the Lie Field of an Algebraic Lie Algebra
- 1 June 1969
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 10 (6) , 975-992
- https://doi.org/10.1063/1.1664944
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 [pi, qj] = δij1 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.Keywords
This publication has 3 references indexed in Scilit:
- Sur l'algébre enveloppante d'une algébre de Lie nilpotenteArchiv der Mathematik, 1959
- Algebraic Lie AlgebrasAnnals of Mathematics, 1947
- A New Kind of Relationship Between MatricesAmerican Journal of Mathematics, 1943