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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