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Article Dans Une Revue Revista de la Unión Matemática Argentina Année : 2023

BROWNIAN MOTION ON INVOLUTIVE BRAIDED SPACES

Uwe Franz
Monika Varšo
  • Fonction : Auteur

Résumé

(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.
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hal-03664273 , version 1 (10-05-2022)

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Uwe Franz, Michael Schürmann, Monika Varšo. BROWNIAN MOTION ON INVOLUTIVE BRAIDED SPACES. Revista de la Unión Matemática Argentina, 2023, 65 (2), pp.495-532. ⟨10.33044/revuma.2574⟩. ⟨hal-03664273⟩
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