Ju n 20 08 Quantum Isometry Groups : Examples and Computations by

In this follow-up of [4], where 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 manifolds including the spheres and the tori. It is also proved that the quantum isometry group of an isospectral deformation of a (classical or noncommutative) manifold is a suitable deformation of the quantum isometry group of the original (undeformed) manifold.

[1]  Debashish Goswami.  Quantum Group of Isometries in Classical and Noncommutative Geometry , 2007, 0704.0041.

[2]  P. Sołtan.  Quantum families of maps and quantum semigroups on finite quantum spaces , 2006, math/0610922.

[3]  T. Banica.  Quantum automorphism groups of homogeneous graphs , 2003, math/0311402.

[4]  T. Banica.  Quantum automorphism groups of small metric spaces , 2003, math/0304025.

[5]  A. Connes,et al.  Institute for Mathematical Physics Noncommutative Finite–dimensional Manifolds Spherical Manifolds and Related Examples Noncommutative Finite-dimensional Manifolds I. Spherical Manifolds and Related Examples , 2022 .

[6]  Shuzhou Wang.  Structure and Isomorphism Classification of Compact Quantum Groups A_u(Q) and B_u(Q) , 1998, math/9807095.

[7]  J. Fröhlich,et al.  Supersymmetric Quantum Theory and Non-Commutative Geometry , 1998, math-ph/9807006.

[8]  Shuzhou Wang,et al.  Quantum Symmetry Groups of Finite Spaces , 1998, math/9807091.

[9]  Ann Maes,et al.  Notes on Compact Quantum Groups , 1998, math/9803122.

[10]  T. Masuda,et al.  Quantum double-torus , 1998, math/9803092.

[11]  Shuzhou Wang.  Deformations of compact quantum groups via Rieffel's quantization , 1996 .

[12]  Shuzhou Wang,et al.  Free products of compact quantum groups , 1995 .

[13]  M. Rieffel.  Deformation Quantization for Actions of R ]D , 1993 .

[14]  P. Podlés.  Symmetries of quantum spaces. Subgroups and quotient . . . , 2008 .

[15]  S. Woronowicz.  Compact quantum groups , 2000 .

[16]  Alain Connes,et al.  Noncommutative geometry , 1994 .

[17]  Sigurdur Helgason,et al.  Topics in Harmonic Analysis on Homogeneous Spaces , 1981 .