Quantum Isometry Groups of Classical and Quantum Spheres
We begin by explicitly computing the quantum isometry groups for the classical spheres and show that these coincide with the commutative \(C^*\) algebra of continuous functions on their classical isometry groups. The rest of the chapter is devoted to the computation of the quantum group of orientation preserving isometries for two different families of spectral triples on the Podles’ spheres, one constructed by Dabrowski et al and the other by Chakraborty and Pal.
KeywordsQuantum Group Strong Operator Topology Compact Quantum Group Quantum Sphere Spectral Triple
- 2.Etingof, P., Goswami, D., Mandal, A., Walton, C.: Hopf coactions on commutative algebras generated by a quadratically independent comodule. Commun. Algebra (To appear). arXiv:1507.08486
- 4.Schmudgen, K., Wagner, E.: Dirac operators and a twisted cyclic cocycle on the standard Podles’ quantum sphere. arXiv:0305051v2
- 6.Bhowmick, J.: Quantum isometry groups. Ph.D thesis, Indian Statistical Institute (2010). arXiv:0907.0618
- 10.Davidson, K.R.: \(C^*\) Algebras by Examples. Hindustan Book Agency (1996)Google Scholar