One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry
Quantum Algebra
2015-11-17 v2 Operator Algebras
Abstract
We prove that under a symmetry assumption all cocycles on Hopf *-algebras arise from generating functionals. This extends earlier results of R.Vergnioux and D.Kyed and has two quantum group applications: all quantum L\'evy processes with symmetric generating functionals decompose into a maximal Gaussian and purely non-Gaussian part and the Haagerup property for discrete quantum groups is characterized by the existence of an arbitrary proper cocycle.
Keywords
Cite
@article{arxiv.1410.6944,
title = {One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry},
author = {Biswarup Das and Uwe Franz and Anna Kula and Adam Skalski},
journal= {arXiv preprint arXiv:1410.6944},
year = {2015}
}
Comments
16 pages; v2 corrects a few minor points. The article has been accepted for publication in Mathematische Zeitschrift