Abstract:

 Let q be a pth root of unity, and L be the derivation Lie algebra over the rank two quantum torus Cq. Let W=Fαg (V) be the L-module define by functor Fαg applied to a finite dimensional gl2-module V. Then the derivations from L to its modules W are most often inner, except for some case, and the first cohomology group H1(L, W) is most often trivial.

Key words: Lie algebra over the quantum torus; module; root of unity; derivation