A note on the von Neumann algebra underlying some universal compact quantum groups.
Equivariant Morita equivalences between Podleś spheres
We show that the family of Podleś spheres is complete under equivariant Morita equivalence (with respect to the action of quantum SU(2)), and determine the associated orbits. We also give explicit formulas for the actions which are equivariantly Morita equivalent with the quantum projective plane. In both cases, the computations are made by examining the localized spectral decomposition of a generalized Casimir element.
Poisson-Lie groupoids and the contraction procedure
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these...
Quantum isometries and group dual subgroups
We study the discrete groups whose duals embed into a given compact quantum group, . In the matrix case the embedding condition is equivalent to having a quotient map , where is a certain family of groups associated to . We develop here a number of techniques for computing , partly inspired from Bichon’s classification of group dual subgroups . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...
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