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Braided quantum SU(2) groups

Paweł Kasprzak, Ralf Meyer, Sutanu Roy, Stanisław Lech Woronowicz

Abstract

We construct a family of q-deformations of SU(2) for complex parameters q not equal to 0. For real q, the deformation coincides with Woronowicz' compact quantum SU_q(2) group. For q not real, SU_q(2) is only a braided compact quantum group with respect to a certain tensor product functor for C*-algebras with an action of the circle group.

Braided quantum SU(2) groups

Abstract

We construct a family of q-deformations of SU(2) for complex parameters q not equal to 0. For real q, the deformation coincides with Woronowicz' compact quantum SU_q(2) group. For q not real, SU_q(2) is only a braided compact quantum group with respect to a certain tensor product functor for C*-algebras with an action of the circle group.

Paper Structure

This paper contains 6 sections, 10 theorems, 57 equations.

Table of Contents

  1. Introduction
  2. The algebra of SUq(2)
  3. Monoidal structure on T-C*-algebras
  4. Proof of the main theorem
  5. The representation theory of SUq(2)
  6. The semidirect product quantum group

Key Result

Theorem 1.1

Let $q\in\mathbb{C}\setminus\{0\}$ and $\zeta=q/\overline{q}$. Then

Theorems & Definitions (18)

  • Theorem 1.1
  • Lemma 2.1
  • Theorem 2.2
  • Theorem 2.3
  • proof
  • Proposition 3.1
  • proof
  • Definition 5.1
  • Proposition 5.2
  • proof
  • ...and 8 more