95 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
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
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 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
A locally compact quantum group of triangular matrices
We construct a one parameter deformation of the group of 2×2 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 C∗-algebra and the dual comultiplication.Побудовано однопараметричну деформацію групи верхніх трикутних матриць розміру 2 × 2 із детермінантом 1 з використанням конструкції скруту. Цікавою рисою цього нового прикладу локально компактної квантової групи є нетривіальна деформація міри Хаара. Наведено також повний опис дуальної C*-алгебри та дуальної комультиплікації
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