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 www.link.springer.com
Uncontrolled Keywords:
?? noncommutative probabilityquantum stochastic compact quantum group c*-bialgebra c*-hyperbialgebra operator space stochastic cocycle quantum levy processmathematics and statisticsmathematical physicsstatistical and nonlinear physicsqa mathematics ??
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Deposited On:
19 Sep 2012 10:55
Last Modified:
21 Apr 2024 00:16