Frontiers of Mathematics in China >
Lie bialgebra structures on derivation Lie algebra over quantum tori
Received date: 20 Jun 2016
Accepted date: 16 Jan 2017
Published date: 06 Jul 2017
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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,W ⊗W) is trivial.
Xiaomin TANG , Lijuan LIU , Jinli XU . Lie bialgebra structures on derivation Lie algebra over quantum tori[J]. Frontiers of Mathematics in China, 2017 , 12(4) : 949 -965 . DOI: 10.1007/s11464-017-0630-7
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