Quantum Group of Orientation preserving Riemannian Isometries

Details Quantum Group of Orientation preserving Riemannian Isometries Quantum Group of Orientation preserving Riemannian Isometries

2008-06-23

arxiv.org/abs/0806.3687v2

Mathematics

Quantum Algebra

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

Scientific paper

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 $SU_\mu(2)$ and $S^2_{\mu 0}$ are dicussed.

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