| Autor: |
Franz, Uwe, Schürmann, Michael, Varso, Monika |
| Přispěvatelé: |
Franz, Uwe, Analyse non commutative sur les groupes et les groupes quantiques - - ANCG2019 - ANR-19-CE40-0002 - AAPG2019 - VALID |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Popis: |
(Quantum) stochastic processes with independent and stationary increments (i.e. Lévy processes) and in particular Brownian motions in braided monoidal categories are studied. The notion of increments is based on a bialgebra or Hopf algebra structure, as in [Sch93], and positivity is taken w.r.t. to an involution. We show that involutive bialgebras and Hopf algebras in the Yetter-Drinfeld categories of a quasi-or coquasi-triangular *-bialgebra admit a symmetrization (or bosonization) and that their Lévy processes are in one-to-one correspondence with a certain class of Lévy processes on their symmetrization. We classify Lévy processes with quadratic generators, i.e., Brownian motions, on several braided Hopf-*-algebras that are generated by their primitive elements (also called braided *-spaces), and on the braided SU (2)-quantum groups. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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