60 citations · 87 across the 8 of their papers we have counts for
9 papers
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…
Hunt's Formula for and
Uwe Franz, Anna Kula, J. Martin Lindsay +1
We provide a Hunt type formula for the infinitesimal generators of Lévy process on the quantum groups and . In particular, we obtain a decomposition of such gener…
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…
Rank two perturbations of matrices and operators and operator model for t-transformation of probability measures
Anna Kula, Michal Wojtylak, Janusz Wysoczański
Rank two parametric perturbations of operators and matrices are studied in various settings. In the finite dimensional case the formula for a characteristic polynomial is derived a…
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…
Woronowicz construction of compact quantum groups for functions on permutations. Classification result for N=3
Anna Kula
We provide a classification of compact quantum groups, which can be obtained by the Woronowicz construction, when the arrays used in the twisted determinant condition are extension…
Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory
Fabio Cipriani, Uwe Franz, Anna Kula
Strongly continuous semigroups of unital completely positive maps (i.e. quantum Markov semigroups or quantum dynamical semigroups) on compact quantum groups are studied. We show th…