Exponential mapping for non semisimple quantum groups

Abstract

The concept of universal T matrix, recently introduced by Fronsdal and Galindo in the framework of quantum groups, is here discussed as a generalization of the exponential mapping. New examples related to inhomogeneous quantum groups of physical interest are developed, the duality calculations are explicitly presented and it is found that in some cases the universal T matrix, like for Lie groups, is expressed in terms of usual exponential series.

12 pages

References in corpus (4)

• Inomogeneous Quantum Groups as Symmetries of Phonons
• Heisenberg XXZ Model and Quantum Galilei Group
• Quantum Galilei Group as Symmetry of Magnons
• The 2-Dimensional Quantum Euclidean Algebra

Cited by in corpus (13)

• Dynamical actions and q-representation theory for double-scaled SYK
• Non-standard quantum (1+1) Poincaré group: a $T$--matrix approach
• Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group
• Finite dimensional representations of the quantum group $G{L}_{p,q}(2)$ using the exponential map from $U_{p,q}(gl(2))$
• Quantum exponentials for the modular double and applications in gravity models
• Coloured quantum universal enveloping algebras
• The exponential map for representations of $U_{p,q}(gl(2))$
• Representation Functions for Jordanian Quantum Group SL_h(2) and Jacobi Polynomials
• SL_q(2,R) at Roots of Unity
• Duals of coloured quantum universal enveloping algebras and coloured universal $\mathcal{T}$-matrices
• Bicrossproduct construction versus Weyl-Heisenberg algebra
• Quantum Galilei group as quantum reference frame transformations
• The dual $(p,q)$-Alexander-Conway Hopf algebras and the associated universal $\mathcal{T}$-matrix