60 citations · 87 across the 8 of their papers we have counts for
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Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras
Isabelle Baraquin, Uwe Franz, Malte Gerhold +2
We find a finite free resolution of the counit of the free unitary quantum groups of van Daele and Wang and, more generally, Bichon's universal cosovereign Hopf algebras with a gen…
Second cohomology groups of the Hopf-algebras associated to universal unitary quantum groups
Biswarup Das, Uwe Franz, Anna Kula +1
We compute the second (and the first) cohomology groups of -algebras associated to the universal quantum unitary groups of not neccesarily Kac type, extending our earlier resul…
Lévy-Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups
Biswarup Das, Uwe Franz, Anna Kula +1
We study the first and second cohomology groups of the -algebras of the universal unitary and orthogonal quantum groups and . This provides valuable information…
Lévy Processes on Quantum Permutation Groups
Uwe Franz, Anna Kula, Adam Skalski
We describe basic motivations behind quantum or noncommutative probability, introduce quantum Lévy processes on compact quantum groups, and discuss several aspects of the study of…
One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry
Biswarup Das, Uwe Franz, Anna Kula +1
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 quan…