26 research outputs found
The bicrossed product construction for locally compact quantum groups
The cocycle bicrossed product construction allows certain freedom in
producing examples of locally compact quantum groups. We give an overview of
some recent examples of this kind having remarkable properties
A locally compact quantum group of triangular matrices
We construct a one parameter deformation of the group of upper
triangular matrices with determinant 1 using the twisting construction. An
interesting feature of this new example of a locally compact quantum group is
that the Haar measure is deformed in a non-trivial way. Also, we give a
complete description of the dual \cs-algebra and the dual comultiplication
On Low-Dimensional Locally Compact Quantum Groups
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.Comment: 64 pages, LaTeX, needs class-file irmadegm.cls. To appear in Locally
Compact Quantum Groups and Groupoids. Proceedings of the Meeting of
Theoretical Physicists and Mathematicians, Strasbourg, February 21 - 23, 200
On Z/2Z-extensions of pointed fusion categories
We give a classification of Z/2Z-graded fusion categories whose 0-component
is a pointed fusion category. A number of concrete examples is considered.Comment: This article will be published by the Banach Center Publication
Twisting and Rieffel's deformation of locally compact quantum groups. Deformation of the Haar measure
We develop the twisting construction for locally compact quantum groups. A
new feature, in contrast to the previous work of M. Enock and the second
author, is a non-trivial deformation of the Haar measure. Then we construct
Rieffel's deformation of locally compact quantum groups and show that it is
dual to the twisting. This allows to give new interesting concrete examples of
locally compact quantum groups, in particular, deformations of the classical
group and of the Woronowicz' quantum group