Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory

@inproceedings{Cipriani2014SymmetriesOL,
  title={Symmetries of L{\'e}vy processes on compact quantum groups, their Markov semigroups and potential theory},
  author={Fabio E.G. Cipriani and Uwe Franz and Anna M. Van Kula},
  year={2014}
}
Quantum Markov semigroups (QMS), i.e. strongly continuous semigroups of unital completely positive maps, on compact quantum groups are studied. We show that translation invariant QMSs on the universal or reduced C⁎-algebra of a compact quantum group are in one-to-one correspondence with Levy processes on its ⁎-Hopf algebra. We use the theory of Levy processes on involutive bialgebras to characterize symmetry properties of the associated QMS. It turns out that the QMS is self-adjoint (resp. KMS… CONTINUE READING

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