On Low-Dimensional Locally Compact Quantum Groups

Details On Low-Dimensional Locally Compact Quantum Groups On Low-Dimensional Locally Compact Quantum Groups

2002-07-29

arxiv.org/abs/math/0207271v1

In "Locally Compact Quantum Groups and Groupoids. Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Str

Mathematics

Quantum Algebra

64 pages, LaTeX, needs class-file irmadegm.cls. To appear in Locally Compact Quantum Groups and Groupoids. Proceedings of the

Scientific paper

Continuing our research on extensions of locally compact quantum groups, we give a classification of all cocycle matched pairs of Lie algebras in small dimensions and prove that all of them can be exponentiated to cocycle matched pairs of Lie groups. Hence, all of them give rise to locally compact quantum groups by the cocycle bicrossed product construction. We also clarify the notion of an extension of locally compact quantum groups by relating it to the concept of a closed normal quantum subgroup and the quotient construction. Finally, we describe the infinitesimal objects of locally compact quantum quantum groups with 2 and 3 generators - Hopf *-algebras and Lie bialgebras.

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