English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove that under a symmetry assumption all cocycles on Hopf *-algebrasarise from generating functionals. This extends earlier results of R.Vergniouxand D.Kyed and has two quantum group applications: all quantum L\'evy processeswith symmetric generating functionals decompose into a maximal Gaussian andpurely non-Gaussian part and the Haagerup property for discrete quantum groupsis characterized by the existence of an arbitrary proper cocycle.

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