On the differential geometry of GLq(1|1)

Abstract

The differential calculus on the quantum supergroup GL(q)(1\1) was introduced by Schmidke et al (1990 Z. Phys. C 48 249). We construct a differential calculus on the quantum supergroup GL(q)(1\1) in a different way and obtain its quantum Lie algebra; The main structures are derived without an R-matrix. It is shown that the results can be written with help of a matrix (R) over cap.