Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 076, 18 pages      arXiv:1307.4850      https://doi.org/10.3842/SIGMA.2014.076
Contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel

Quantum Isometry Groups of Noncommutative Manifolds Obtained by Deformation Using Dual Unitary 2-Cocycles

Debashish Goswami and Soumalya Joardar
Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India

Received January 29, 2014, in final form July 11, 2014; Published online July 17, 2014

Abstract
It is proved that the (volume and orientation-preserving) quantum isometry group of a spectral triple obtained by deformation by some dual unitary 2-cocycle is isomorphic with a similar twist-deformation of the quantum isometry group of the original (undeformed) spectral triple. This result generalizes similar work by Bhowmick and Goswami for Rieffel-deformed spectral triples in [Comm. Math. Phys. 285 (2009), 421-444].

Key words: cocycle twist; quantum isometry group; Rieffel deformation; spectral triple.

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