On the q-deformation of certain infinite dimensional Lie algebras

A representation of the q-deformed centreless Virasoro algebra in terms of the Gauss derivatives Dx and Dy on the quantum plane Cq[x, y] is given. Moreover, we obtain the deformed version of the algebra of the area-preserving diffeomorphisms of the torus T2. In the end, the correspondence between Psd (q, p, r) and the ā∞ algebra is pointed out.