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arXiv · 1410.6944

One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry

Biswarup Das·Uwe Franz·Anna Kula·Adam Skalski
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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 Lévy 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.

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Biswarup Das, Uwe Franz, Anna Kula, Adam Skalski. 2015-06-23. One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry. https://doi.org/10.1007/s00209-015-1515-7

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