Quantum Isometry Group for Spectral Triples with Real Structure

Abstract

Given a spectral triple of compact type with a real structure in the sense of [Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of Connes' original definition to accommodate examples coming from quantum group theory) and references therein, we prove that there is always a universal object in the category of compact quantum group acting by orientation preserving isometries (in the sense of [Bhowmick J., Goswami D., J. Funct. Anal. 257 (2009), 2530-2572]) and also preserving the real structure of the spectral triple. This gives a natural definition of quantum isometry group in the context of real spectral triples without fixing a choice of 'volume form' as in [Bhowmick J., Goswami D., J. Funct. Anal. 257 (2009), 2530-2572].

References in corpus (3)

• Quantum families of maps and quantum semigroups on finite quantum spaces
• Quantum Isometry Groups of 0- Dimensional Manifolds
• Quantum Isometry Groups: Examples and Computations

Cited by in corpus (4)

• Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations
• Quantum isometry groups of noncommutative manifolds associated to group C*-algebras
• Quantum Isometries of the finite noncommutative geometry of the Standard Model
• Isometric coactions of compact quantum groups on compact quantum metric spaces