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 = 0). The correspondent curvature is derived and the related non-commutative gauge field theory is introduced.PACS. 02.20.Uw, 02.40.Gh.