Lie Bialgebra Structure of Derivation Lie Algebra over Quantum Torus

Abstract

In this paper, all Lie bialgebra structures on the derivation Lie algebra W over a rank $d\ge 3$ quantum torus associated to q are considered, where q is a $d\times d$ matrix with all the entries being roots of unity. They are shown to be triangular coboundary. As a byproduct, it is also proved that the first cohomology group $H^1(W,W\otimes W)$ is trivial.

Keywords

Lie bialgebras / Lie coalgebras / Yang–Baxter equation / quantum torus

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