Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

An De Rijdt; Nikolas Vander Vennet

Displaying similar documents to “Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries”

Invariants of the half-liberated orthogonal group

Teodor Banica, Roland Vergnioux (2010)

Annales de l’institut Fourier

Similarity:

The half-liberated orthogonal group $O_{n}^{*}$ appears as intermediate quantum group between the orthogonal group $O_{n}$ , and its free version $O_{n}^{+}$ . We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between $O_{n}^{*}$ and $U_{n}$ , a non abelian discrete group playing the role of weight lattice, and a number of methods inspired from the theory of Lie algebras. We use these results for...

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 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...

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:

Quantum isometry group for spectral triples with real structure.

Goswami, Debashish (2010)

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

Similarity:

Graphs having no quantum symmetry

Teodor Banica, Julien Bichon, Gaëtan Chenevier (2007)

Annales de l’institut Fourier

Similarity:

We consider circulant graphs having $p$ vertices, with $p$ prime. To any such graph we associate a certain number $k$ , that we call type of the graph. We prove that for $p ≫ k$ the graph has no quantum symmetry, in the sense that the quantum automorphism group reduces to the classical automorphism group.

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.