Differential geometry of GL${}_{p,q}(1|1)$

Abstract

We introduce a construction of the differential calculus on the quantum supergroup GL${}_{p,q}(1|1)$. We obtain two differential calculi, respectively, associated with the left and right Cartan-Maurer one-forms. We also obtain the quantum superalgebra of GL${}_{p,q}(1|1)$. Although all of the structures we obtain are derived without an R matrix, they neverthless can be expressed using an R matrix.

19 pages

References in corpus (3)

• On the Differential Geometry of $G{L}_q(1|1)$
• Two parameter deformation of Grassmann matrix group and supergroup
• Hopf algebra structure of Gr${}_q(1|1)$ related to GL${}_q(1|1)$