Non-Semi-Regular Quantum Groups Coming from Number Theory

By Saad Baaj, G. Skandalis, S. Vaes. 2002

83 citations recorded by the source corpus.

Abstract: In this paper, we study C*-algebraic quantum groups obtained through the bicrossed product construction. Examples using groups of adeles are given and they provide the first examples of locally compact quantum groups which are not semi-regular: the crossed product of the quantum group acting on itself by translations does not contain any compact operator. We describe all corepresentations of these quantum groups and the associated universal C*-algebras. On the way, we provide several remarks on C*-algebraic properties of quantum groups and their actions.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cb2147e22d467ab7b036987aef01cbc482992d85

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. S. Vaes
2. Matthew Daws
3. Amaury Freslon
4. Christian Voigt

In Mathematical Physics

1. Saad Baaj
2. Matthew Daws
3. S. Vaes
4. K. De Commer
5. Adrian Ioana
6. Sorin Popa
7. A. Furman
8. Martijn Caspers

Citations in the corpus

• Multipliers, Self-Induced and Dual Banach Algebras (2010, background): “If M = L(G) or V N(G) (or, more generally, is a Kac algebra) then W is regular, but there do exists locally compact quantum groups for which W is not regular, see [1].”
• DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS (2002, background): “quantum groups are semi-regular (see [3]).”
• Strictly Outer Actions of Groups and Quantum Groups (2002, unknown): “O A ] 2 3 M ay 2 00”