Quantum Isometry Group for Spectral Triples with Real Structure

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 refe- rences 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).

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