Quantum Isometry Group for Spectral Triples with Real Structure

Symmetry Integrability and Geometry-Methods and Applications

article

Debashish Goswami¹ 

[1] Stat-Math Unit, Indian Statistical Institute

关键词: quantum isometry groups;    spectral triples;    real structures;   

DOI  :  10.3842/SIGMA.2010.007

来源: National Academy of Science of Ukraine

【 摘 要 】

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].

【 授权许可】

Unknown