Quantum group of orientation-preserving Riemannianisometries

摘要

We formulate a quantum group analogue of the group of orientation-preserving Riemannian isometriesof a compact Riemannian spin manifold, more generally, of a (possibly R-twisted and of compact type)spectral triple. The main advantage of this formulation, which is directly in terms of the Dirac operator, isthat it does not need the existence of any ‘good' Laplacian as in our previous works on quantum isometrygroups. Several interesting examples, including those coming from Rieffel-type deformation as well as theequivariant spectral triples on SU_μ (2) and S_(μ,c)~2are discussed.