Compact quantum groups

Topisc covered

1. The Hopf \(*\)-algebra of polynomial functions on \(\mathrm{SU}(2)\) and its \(q\)-deformation
2. C*-algebras, theorems of Gelfand and Gelfand-Naimark, tensor products
3. Positive elements, state, the GNS construction
4. Definition of a compact quantum group, examples, compact matrix quantum groups

Lecture notes

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4

Recommended literature

1. S.L. Woronowicz - Compact matrix pseudogroups. LINK
2. S.L. Woronowicz - Compact quantum groups. LINK
3. S. Neshveyev, L. Tuset - Compact quantum groups and their representation categories
4. P. Podleś, E. Müller - Introduction to quantum groups. arXiv | DOI
5. A. Maes, A. Van Daele - Notes on compact quantum groups arXiv
6. U. Franz, A. Skalski, P.M. Sołtan - Introduction to compact and discrete quantum groups. arXiv | DOI