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21 juin 2022: 1 événement

  • Séminaire d’Analyse Fonctionnelle

    Mardi 21 juin 13:45-14:45 - Juan Galvis Salazar - Lancaster University

    Lévy Processes on Compact Quantum Groups

    Résumé : This talk will be split in two parts. The first one will be dedicated to introducing the definitions of compact quantum groups in the sense of Woronowicz, and some objects of noncommutative probability. In the second one it will be extended the purely algebraic setting of noncommutative Lévy processes to the analytic case by simply exploiting the fact that in the classical version the whole information is encoded in the corresponding convolution semigroup. In fact, we prove that Lévy processes on compact quantum groups actually exist via the generalization of the theory set by Hudson and Parthasarathy. Further, an analogue to the characterization of Lévy processes on involutive bialgebras, made by means of Schürmann’s theory, will be presented for the context of compact quantum groups. Finally, it is shown that there exists a one-to-one correspondence between norm continuous quantum Lévy processes and the Fock-space ones.

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