Quantum Group of Orientation preserving Riemannian Isometries

Abstract

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 paper of one of the authors, and of compact type) spectral triple. The main advantage of this formulation, which is directly in terms of the Dirac operator, is that it does not need the existence of any `good ' Laplacian as in our previous works on quantum isometry groups. Several interesting examples, including those coming from Rieffel-type deformation as well as the equivariant spectral triples on $S{U}_{\mu }(2)$ and $S_{\mu 0}^2$ are dicussed.

Substantially improved and revised version. In particular, subsection 2.3 and Section 3 are new

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Cited by in corpus (5)

• Non-Commutative Geometry, Categories and Quantum Physics
• Quantum Isometry Groups of 0- Dimensional Manifolds
• Classification results for easy quantum groups
• Quantum symmetries of classical spaces
• On the problem of classifying simple compact quantum groups