HOPF ALGEBRA STRUCTURE OF (2+1)-DIMENSIONAL QUANTUM SUPERSPACE, ITS DUAL AND ITS DIFFERENTIAL CALCULUS

Abstract

We consider a (2 +1)-dimensional quantum superspace which has noncommuting coordinates in Martin sense and it was shown that this space has a Hopf algebra structure, i.e., the quantum supergroup, when it is extended by the inverse of the bosonic variable. Differential structures on this space were given by constructing the differential calculus in the sense of Woronowicz. This, we deduce that the corresponding quantum Lie super-algebra which as a commutation superalgebra appears classical, and as Hopf structure is non-cocommutative q-deformed. Finally, dual Hopf superalgebra was given.