Quantum isometries and group dual subgroups

Teodor Banica; Jyotishman Bhowmick; Kenny De Commer

Displaying similar documents to “Quantum isometries and group dual subgroups”

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 ${σ_{z}}_{z \in ℂ}$ acting on . It turns...

New solutions for Yang-Baxter systems.

Nichita, Florin Felix (2006)

Acta Universitatis Apulensis. Mathematics - Informatics

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Quantum Painlevé equations: from continuous to discrete.

Nagoya, Hajime, Grammaticos, Basil, Ramani, Alfred (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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A Note on Free Quantum Groups

Teodor Banica (2008)

Annales mathématiques Blaise Pascal

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We study the free complexification operation for compact quantum groups, $G \to G^{c}$ . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying $G = G^{c}$ .

On quantum weyl algebras and generalized quons

WŁadysŁaw Marcinek (1997)

Banach Center Publications

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The model of generalized quons is described in an algebraic way as certain quasiparticle states with statistics determined by a commutation factor on an abelian group. Quantization is described in terms of quantum Weyl algebras. The corresponding commutation relations and scalar product are also given.

$κ$ -Minkowski spacetimes and DSR algebras: fresh look and old problems.

Borowiec, Andrzej, Pachol, Anna (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Left-covariant differential calculi on $S L_{q} (N)$

Konrad Schmüdgen, Axel Schüler (1997)

Banach Center Publications

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We study $N^{2} - 1$ dimensional left-covariant differential calculi on the quantum group $S L_{q} (N)$ . In this way we obtain four classes of differential calculi which are algebraically much simpler as the bicovariant calculi. The algebra generated by the left-invariant vector fields has only quadratic-linear relations and posesses a Poincaré-Birkhoff-Witt basis. We use the concept of universal (higher order) differential calculus associated with a given left-covariant first order differential calculus....

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...

Statistics and quantum group symmetries

Gaetano Fiore, Peter Schupp (1997)

Banach Center Publications

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Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.