A star-product approach to noncompact quantum groups

TL;DR

This paper develops star-product models for noncompact quantum groups using duality and topological Hopf algebra theory, extending their applicability to all smooth functions and non-linear Lie groups.

Contribution

It introduces a novel star-product construction for noncompact quantum groups based on duality and topological Hopf algebra methods, applicable to all smooth functions.

Findings

Star-products act on all $C^ abla$ functions.

Existence of star-products for non-linear Lie groups.

Applicable to Drinfeld and Reshetikhin deformations.

Abstract

Using duality and topological theory of well behaved Hopf algebras (as defined in [2]) we construct star-product models of non compact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple Lie algebras. Our star-products act not only on coefficient functions of finite-dimensional representations, but actually on all $C^\infty$ functions, and they exist even for non linear (semi-simple) Lie groups.