Displaying similar documents to “The unitary implementation of a measured quantum groupoid action”

Quantum symmetries in noncommutative C*-systems

Marcin Marciniak (1998)

Banach Center Publications

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We introduce the notion of a completely quantum C*-system (A,G,α), i.e. a C*-algebra A with an action α of a compact quantum group G. Spectral properties of completely quantum systems are investigated. In particular, it is shown that G-finite elements form the dense *-subalgebra of A. Furthermore, properties of ergodic systems are studied. We prove that there exists a unique α-invariant state ω on A. Its properties are described by a family of modular operators σ z z ∈ ℂ acting on . It turns...

Quantum Itô B*-algebras, their classification and decomposition

V. Belavkin (1998)

Banach Center Publications

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A simple axiomatic characterization of the general (infinite dimensional, noncommutative) Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Itô B*-algebra, generalizing the C*-algebra, is defined to include the Banach infinite dimensional Itô algebras of quantum Brownian and quantum Lévy motion, and the B*-algebras of vacuum and thermal quantum noise are characterized. It is proved that every Itô algebra is canonically...

Quantum isometries and group dual subgroups

Teodor Banica, Jyotishman Bhowmick, Kenny De Commer (2012)

Annales mathématiques Blaise Pascal

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We study the discrete groups Λ whose duals embed into a given compact quantum group, Λ ^ ⊂ G . In the matrix case G ⊂ U n + the embedding condition is equivalent to having a quotient map Γ U → Λ , where F = { Γ U ∣ U ∈ U n } is a certain family of groups associated to G . We develop here a number of techniques for computing F , partly inspired from Bichon’s classification of group dual subgroups Λ ^ ⊂ S n + . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot...