Lie bialgebra structures on derivation Lie algebra over quantum tori

被引：3

作者：

Tang, Xiaomin ^{[1
]}

Liu, Lijuan ^{[2
]}

Xu, Jinli ^{[3
]}

机构：

[1] Heilongjiang Univ, Dept Math, Harbin 150080, Peoples R China

[2] Harbin Inst Technol Press, Harbin 150001, Peoples R China

[3] Northeast Forestry Univ, Dept Math, Harbin 150040, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2017年 / 12卷 / 04期

基金：

黑龙江省自然科学基金; 中国国家自然科学基金;

关键词：

Lie bialgebra; Yang-Baxter equation; derivation Lie algebra over quantum tori; CENTRAL EXTENSIONS; VIRASORO ALGEBRAS; REPRESENTATIONS; WITT; CLASSIFICATION;

D O I：

10.1007/s11464-017-0630-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate Lie bialgebra structures on the derivation Lie algebra over the quantum torus. It is proved that, for the derivation Lie algebra W over a rank 2 quantum torus, all Lie bialgebra structures on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H (1)(W, W aSu W) is trivial.

引用

页码：949 / 965

页数：17

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