BEN GURION UNIVERSITY OF THE NEGEV
DEPARTMENT OF MATHEMATICS
Operator and System Theory Seminar
SPEAKER: Ami Viselter, University of Alberta
TITLE: Locally compact quantum groups and amenability
DATE: Monday, January 2, 2012
PLACE: Room -101, Mathematics Building, BGU
The concept of group duality is one of the most fundamental ones
in the analysis of abelian, locally compact groups.
The theory of quantum groups was initially developed
in order to provide a framework for duality of general locally compact groups.
The first such framework, called Kac algebras, turned out to be
too restrictive when more and more examples of "quantum" groups emerged,
which didn't fit into this category. Other collections of axioms, defining
so-called quantum groups (in a broader sense), were therefore sought.
Building on the preceding, deep work of Kac and Vainerman, Enock and Schwartz,
Woronowicz and Baaj and Skandalis (to name a few), Kustermans and Vaes suggested
in 1999 a relatively simple set of axioms for "locally compact quantum
groups" (LCQGs). In this talk we will introduce their definition,
show the basic examples, and discuss a few specific types of LCQGs.
Afterwards, we will review the definition of amenability for locally
compact groups, present its generalization(s) to LCQGs, and relate several
problems of current research connected with these notions.
All relevant terms will be defined/sketched during the talk; we will
only assume familiarity with "standard" functional analysis.
In particular, no prior knowledge of harmonic analysis or
(algebraic) quantum groups is required.
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