Measured quantum groupoids

Details Measured quantum groupoids Measured quantum groupoids

2004-09-21

arxiv.org/abs/math/0409380v1

Mathematics

Operator Algebras

Scientific paper

In this article, part of the author's thesis, we propose a definition for measured quantum groupoid. The aim is the construction of objects with duality including both quantum groups and groupoids. We base ourselves on J. Kustermans and S. Vaes' works about locally compact quantum groups that we generalize thanks to formalism introduced by M. Enock and J.M. Vallin in the case of inclusion of von Neumann algebras. From a structure of Hopf-bimodule with left and right invariant operator-valued weights, we define a fundamental pseudo-multiplicative unitary. We introduce the notion of quasi-invariant weight on the basis and, then, we construct an antipode with polar decomposition, a coinvolution, a scaling group, a modulus and a scaling operator. This theory is illustrated with different examples. Duality of measured quantum groupoids will be discussed in a forthcoming article.

Affiliated with

Also associated with

No associations

Rating

Measured quantum groupoids 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 Measured quantum groupoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Measured quantum groupoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-327902