Non-commutative differential calculus and q-analysis

Abstract

Starting from the formulation of covariant noncommutative differential calculus recently given by Wess and Zumino (1990) the author constructs a deformation of the Virasoro algebra, which allows him to identify the variables and differential operators on the quantum plane R2q to those on the classical plane R2. This correspondence indicates how noncommutative geometry can be understood in terms of q-analysis on the commutative plane. He generalizes this result to the general n-dimensional case and discuss some of its consequences.