The Two-Parameter Higher Order Differential Calculus and Curvature on a Quantum Plane

Abstract

We construct an associative differential algebra on a two-parameter quantum plane associated with a nilpotent endomorphism $d$ in the two cases $d^2=0$ and $d^3=0$ $(d^2\ne 0).$ The correspondent curvature is derived and the related non commutative gauge field theory is introduced.

11 pages