Quantum Isometry Group for Spectral Triples with Real Structu

Given a spectral triple of compact type with a real structure in the sense of [Dąbrowski 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].