Free dynamical quantum groups and the dynamical quantum group SU_q(2)

TL;DR

This paper introduces dynamical versions of free quantum groups, transforming them into Hopf algebroids, and provides algebraic and C*-algebraic constructions, including a refined dynamical SU_q(2) with notable limit cases.

Contribution

It develops dynamical analogues of free orthogonal and unitary quantum groups as Hopf algebroids, extending their algebraic and C*-algebraic frameworks.

Findings

Constructed dynamical free orthogonal and unitary quantum groups

Recovered and refined the dynamical SU_q(2)

Included several interesting limit cases

Abstract

We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the level of universal C*-algebras. As an example, we recover the dynamical SU_q(2) studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.