Mathematics – Quantum Algebra
Scientific paper
2008-11-02
Mathematics
Quantum Algebra
substantial changes: the prof of necessity of Kac algebra condition is completely new; it replaces the earlier proof which was
Scientific paper
We prove that a compact quantum group with faithful Haar state which has a faithful action on a compact space must be a Kac algebra, with bounded antipode and the square of the antipode being identity. The main tool in proving this is the theory of ergodic quantum group action on $C^*$ algebras. Using the above fact, we also formulate a definition of isometric action of a compact quantum group on a compact metric space, generalizing the definition given by Banica for finite metric spaces, and prove for certain special class of metric spaces the existence of the universal object in the category of those compact quantum groups which act isometrically and are `bigger' than the classical isometry group.
No associations
LandOfFree
Quantum symmetries and quantum isometries of compact metric spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum symmetries and quantum isometries of compact metric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum symmetries and quantum isometries of compact metric spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-248629