On the Differential Geometry of $GL_q(1| 1)$

Details On the Differential Geometry of $GL_q(1| 1)$ On the Differential Geometry of $GL_q(1| 1)$

2001-12-12

arxiv.org/abs/math/0112123v1

J. Phys. A: Math. Gen. 31 (1998), 9685-9694

Mathematics

Quantum Algebra

14 pages

Scientific paper

10.1088/0305-4470/31/48/005

The differential calculus on the quantum supergroup GL$_q(1| 1)$ was introduced by Schmidke {\it et al}. (1990 {\it Z. Phys. C} {\bf 48} 249). We construct a differential calculus on the quantum supergroup GL$_q(1| 1)$ in a different way and we obtain its quantum superalgebra. The main structures are derived without an R-matrix. It is seen that the found results can be written with help of a matrix $\hat{R}$

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