Non-semi-regular quantum groups coming from number theory

Details Non-semi-regular quantum groups coming from number theory Non-semi-regular quantum groups coming from number theory

2002-09-06

arxiv.org/abs/math/0209069v1

Communications in Mathematical Physics 235 (1) (2003), 139-167.

Mathematics

Operator Algebras

25 pages LaTeX

Scientific paper

10.1007/s00220-002-0780-6

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.

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