Extensions and contractions of the Lie algebra of q-pseudodifferential symbols on the circle

被引：47

作者：

Khesin, B

Lyubashenko, V

Roger, C

机构：

[1] UNIV YORK,DEPT MATH,YORK YO1 5DD,N YORKSHIRE,ENGLAND

[2] UNIV LYON 1,INST GIRARD DESARGUES,URA 746,F-69622 VILLEURBANNE,FRANCE

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1997年 / 143卷 / 01期

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

D O I：

10.1006/jfan.1996.2896

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct cocycles on the Lie algebra of pseudo- and q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ''quantum'' Godbillon-Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand-Fuchs 3-cocycle on periodic vector fields. A nontrivial embedding of the Virasoro algebra into (a completion of) q-pseudodifferential symbols is proposed. We describe q-analogs of the KP and KdV-hierarchies admitting an infinite number of conserved charges as well as q-deformed Gelfand-Dickey structures. (C) 1997 Academic Press

引用

页码：55 / 97

页数：43

共 41 条

[21] SPIN AND WEDGE REPRESENTATIONS OF INFINITE-DIMENSIONAL LIE-ALGEBRAS AND GROUPS - (CLIFFORD ALGEBRA-SPIN REPRESENTATION-AFFINE KAC-MOODY LIE ALGEBRA-HIGHEST WEIGHT REPRESENTATION-LINE BUNDLE) [J].