Three levels in the theory of quantum groups
- Stanislaw Lech Woronowicz (Warsaw University, Warsaw, Poland)
Abstract
Quantum groups may be considered on three levels. On the Hopf algebra (or Hopf *-algebra) level we deal with polynomial functions on the group. Quantum groups appears as deformations of classical algebraic groups. One the other side we have C*-level. On this level we work with quantum versions of locally compact topological groups and the concepts and methods of functional analysis are intensively used. In between we have Hilbert space level, where we deal with closed operators acting on a Hilbert space which are interpreted as coordinates on quantum groups.
With a number of examples we shall discuss the characteristic features of each level and the relations between the levels. In particular the speaker hopes to attract the listeners attention to the Hilbert space level.
