Bicovariant Differential Geometry of the Quantum Group $S{L}_h(2)$

Abstract

There are only two quantum group structures on the space of two by two unimodular matrices, these are the $S{L}_q(2)$ and the $S{L}_h(2)$ [9-13] quantum groups. One can not construct a differential geometry on $S{L}_q(2)$, which at the same time is bicovariant, has three generators, and satisfies the Liebnitz rule. We show that such a differential geometry exists for the quantum group $S{L}_h(2)$ and derive all of its properties.

References in corpus (4)

• An introduction to non-commutative differential geometry on quantum groups
• Differential Geometry on Linear Quantum Groups
• The 2-Parametric Extension of $h$ Deformation of $GL(2)$, and The Differential Calculus on Its Quantum Plane
• The quantum de Rham complexes associated with $S{L}_h(2)$

Cited by in corpus (6)

• Classification of Left-Covariant Differential Calculi on the Quantum Group $\SLq 2$
• Duality for Exotic Bialgebras
• Representation Functions for Jordanian Quantum Group SL_h(2) and Jacobi Polynomials
• Classification of bicovariant differential calculi on the Jordanian quantum groups GL_{g,h}(2) and SL_{h}(2) and quantum Lie algebras
• Maps between Deformed and Ordinary Gauge Fields
• Differential geometry of GL${}_h(1|1)$