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

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

2001-12-06

arxiv.org/abs/math/0112059v1

J. Math. Phys. 41 (2000), 6976-6994

Mathematics

Quantum Algebra

19 pages

Scientific paper

10.1063/1.1285032

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.

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