Lie bialgebra structures on derivation Lie algebra over quantum tori

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,W ⊗W) is trivial.

Keywords

Lie bialgebra / Yang-Baxter equation / derivation Lie algebra over quantum tori

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2017 Higher Education Press and Springer-Verlag Berlin Heidelberg