Differential Geometry of the Lie Superalgebra of the Quantum Superplane

Noncommutative differential geometry has attracted considerable interest both mathematically and also from theoretical physics side over the past decade. Especially, there is much activity in differential geometry on quantum groups. For references to the literature for quantum groups we refer to the recent book by Majid [1]. The basic structure giving a direction to the noncommutative geometry is a differential calculus on an associative algebra. A noncommutative differential calculus on quantum groups has been introduced by Woronowicz [2]. Wess and Zumino [3] has been reformulated to fit this general theory, in less abstract way. Some other methods to define a differential geometric structure (or a De Rham complex) on a given noncommutative associative algebra or to construct a noncommutative geometry on a quantum group have been proposed and investigated by several authors [4-9]. E-mail address: [email protected]