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.
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页码：949 / 965
页数：17
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