DIFFERENTIAL GEOMETRY OF THE QUANTUM SUPERGROUP GLH,H' (1|1)

Abstract

In this paper, we construct a bi-covariant (h, h')-deformed differential calculus on the Hopf superalgebra of functions on the quantum supergroup GL(h,h')(1|1) and obtain an extended differential calculus (Cartan calculus) by including inner derivations and Lie derivatives. In doing so, we use left-Cartan-Maurer 1-forms and left-vector fields.