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Quantum stochastic convolution cocycles II

Lindsay, J. Martin and Skalski, Adam G. (2008) Quantum stochastic convolution cocycles II. Communications in Mathematical Physics, 280 (3). pp. 575-610. ISSN 0010-3616

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    Schurmann's theory of quantum Levy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic convolution cocycles on a C*-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic differential equations with completely bounded coefficients, and the structure of their stochastic generators is obtained. Automatic complete boundedness of a class of derivations is established, leading to a characterisation of the stochastic generators of *-homomorphic convolution cocycles on a C*-bialgebra. Two tentative definitions of quantum Levy process on a compact quantum group are given and, with respect to both of these, it is shown that an equivalent process on Fock space may be reconstructed from the generator of the quantum Levy process. In the examples presented, connection to the algebraic theory is emphasised by a focus on full compact quantum groups.

    Item Type: Journal Article
    Journal or Publication Title: Communications in Mathematical Physics
    Additional Information: The original publication is available at
    Uncontrolled Keywords: Noncommutative probability ; quantum stochastic ; compact quantum group ; C*-bialgebra ; C*-hyperbialgebra ; operator space ; stochastic cocycle ; quantum Levy process
    Subjects: ?? qa ??
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 58402
    Deposited By: ep_importer_pure
    Deposited On: 19 Sep 2012 11:55
    Refereed?: Yes
    Published?: Published
    Last Modified: 18 Jun 2018 00:19
    Identification Number:

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