GELFAND-KIRILLOV CONJECTURE ON LIE FIELD OF AN ALGEBRAIC LIE ALGEBRA

被引：12

作者：

CHOW, Y

机构：

[1] Department of Physics, University of Wisconsin, Milwaukee, WI

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 1969年 / 10卷 / 06期

关键词：

D O I：

10.1063/1.1664944

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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, q i] = 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.

引用

页码：975 / &

共 15 条

[1] ALGEBRAIC LIE ALGEBRAS
CHEVALLEY, C
[J]. ANNALS OF MATHEMATICS, 1947, 48 (01) : 91 - 100
[2] A new kind of relationship between matrices
Chevalley, C
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1943, 65 : 521 - 531
[3] CHEVALLEY C, 1955, THEORIE GROUPES LIE, V2
[4] Dixmier J., 1959, ARCH MATH, V10, P321, DOI [10.1007/BF01240805, DOI 10.1007/BF01240805]
[5] Dixmier J., 1957, B SMF, V85, P325
[6] Gelfand I. M., 1966, SOV MATH, V167, P503
[7] GELFAND IM, 1966, DOKL AKAD NAUK SSSR+, V167, P503
[8] GELFAND IM, 1950, MATHEMATICAL SURVEY, V26, P193
[9] KIRILLOV AA, 1961, DOKL AKAD NAUK SSSR+, V138, P283
[10] KIRILLOV AA, 1960, DOKL AKAD NAUK SSSR+, V130, P966

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