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Quantum Group of Orientation preserving Riemannian Isometries
We formulate a quantum group analogue of the group of orinetation-preserving Riemannian isometries of a compact Riemannian spin manifold, more generally, of a (possibly $R$-twisted in the sense of a
Quantum Isometry Groups: Examples and Computations
In this follow-up of [4], where the quantum isometry group of a noncommutative manifold has been defined, we explicitly compute such quantum groups for a number of classical as well as noncommutative
Quantum isometry groups of noncommutative manifolds associated to group C∗-algebras
Abstract Let Γ be a finitely generated discrete group. The standard spectral triple on the group C ∗ -algebra C ∗ ( Γ ) is shown to admit the quantum group of orientation preserving isometries. This
Compact quantum metric spaces from quantum groups of rapid decay
We present a modified version of the definition of property RD for discrete quantum groups given by Vergnioux in order to accommodate examples of non-unimodular quantum groups. Moreover we extend the
Quantum isometries and group dual subgroups
We study the discrete groups $\Lambda$ whose duals embed into a given compact quantum group, $\hat{\Lambda}\subset G$. In the matrix case $G\subset U_n^+$ the embedding condition is equivalent to
Deformation of operator algebras by Borel cocycles
Assume that we are given a coaction \delta of a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle \omega on G. Motivated by the approach of Kasprzak to Rieffel's deformation we
Quantum isometry group of the n-tori
We show that the quantum isometry group (introduced by Goswami) of the n-tori T n coincides with its classical isometry group; i.e. there does not exist any faithful isometric action on T n by a
Quantum Isometries of the Finite Noncommutative Geometry of the Standard Model
We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine
Quantum Isometry Groups
In the memory of my grandmother Acknowledgements I would like to start by expressing my deepest gratitudes to my supervisor Debashish Goswami who introduced me to the theories of noncommutative
Levi-Civita connections for a class of spectral triples
We give a new definition of Levi-Civita connection for a noncommutative pseudo-Riemannian metric on a noncommutative manifold given by a spectral triple. We prove the existence–uniqueness result for