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Frontiers of Mathematics in China

Front. Math. China    2017, Vol. 12 Issue (4) : 949-965     DOI: 10.1007/s11464-017-0630-7
RESEARCH ARTICLE |
Lie bialgebra structures on derivation Lie algebra over quantum tori
Xiaomin TANG1(), Lijuan LIU2, Jinli XU3
1. Department of Mathematics, Heilongjiang University, Harbin 150080, China
2. Harbin Institute of Technology Press, Harbin 150001, China
3. Department of Mathematics, Northeast Forestry University, Harbin 150040, China
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Abstract

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 H1(W,WW) is trivial.

Keywords Lie bialgebra      Yang-Baxter equation      derivation Lie algebra over quantum tori     
Corresponding Authors: Xiaomin TANG   
Issue Date: 06 July 2017
 Cite this article:   
Xiaomin TANG,Lijuan LIU,Jinli XU. Lie bialgebra structures on derivation Lie algebra over quantum tori[J]. Front. Math. China, 2017, 12(4): 949-965.
 URL:  
http://journal.hep.com.cn/fmc/EN/10.1007/s11464-017-0630-7
http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/949
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Xiaomin TANG
Lijuan LIU
Jinli XU
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