Exponential mapping for non semisimple quantum groups

TL;DR

This paper explores the exponential mapping in the context of non-semisimple quantum groups, generalizing the universal T matrix concept and providing new examples related to inhomogeneous quantum groups with explicit duality calculations.

Contribution

It introduces a generalized exponential mapping for non-semisimple quantum groups and presents new examples and duality calculations, expanding the understanding of universal T matrices.

Findings

Universal T matrix can be expressed as usual exponential series in some cases

New examples of inhomogeneous quantum groups are developed

Explicit duality calculations are provided

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.