Groupoids and compact quantum groups

Albert Sheu

Displaying similar documents to “Groupoids and compact quantum groups”

Algebraic topology foundations of supersymmetry and symmetry breaking in quantum field theory and quantum gravity: a review.

Baianu, Ion C., Glazebrook, James F., Brown, Ronald (2009)

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

Similarity:

The unitary implementation of a measured quantum groupoid action

Michel Enock (2010)

Annales mathématiques Blaise Pascal

Similarity:

Mimicking the von Neumann version of Kustermans and Vaes’ locally compact quantum groups, Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In a former article, the author had introduced the notions of actions, crossed-product, dual actions of a measured quantum groupoid; a biduality theorem for actions has been proved. This article continues that program: we prove the existence of a standard implementation for an action, and...

Morita equivalence of measured quantum groupoids. Application to deformation of measured quantum groupoids by 2-cocycles

Michel Enock (2012)

Banach Center Publications

Similarity:

In a recent article, Kenny De Commer investigated Morita equivalence between locally compact quantum groups, in which a measured quantum groupoid, of basis ℂ², was constructed as a linking object. Here, we generalize all these constructions and concepts to the level of measured quantum groupoids. As for locally compact quantum groups, we apply this construction to the deformation of a measured quantum groupoid by a 2-cocycle.

Quantum isometries and group dual subgroups

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

Annales mathématiques Blaise Pascal

Similarity:

We study the discrete groups $Λ$ whose duals embed into a given compact quantum group, $\hat{Λ} \subset G$ . In the matrix case $G \subset U_{n}^{+}$ the embedding condition is equivalent to having a quotient map $Γ_{U} \to Λ$ , where $F = {Γ_{U} ∣ U \in U_{n}}$ 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 $\hat{Λ} \subset S_{n}^{+}$ . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot...

$κ$ -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]

Similarity:

On quantum weyl algebras and generalized quons

WŁadysŁaw Marcinek (1997)

Banach Center Publications

Similarity:

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.

Quantum symmetries in noncommutative C*-systems

Marcin Marciniak (1998)

Banach Center Publications

Similarity:

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...

Quantum Painlevé equations: from continuous to discrete.

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

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

Similarity:

Statistics and quantum group symmetries

Gaetano Fiore, Peter Schupp (1997)

Banach Center Publications

Similarity:

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.