Some counterexamples in the Theory of Quantum Isometry groups

Bhowmick, Jyotishman ; Goswami, Debashish (2010) Some counterexamples in the Theory of Quantum Isometry groups Letters in Mathematical Physics, 93 (3). pp. 279-293. ISSN 0377-9017

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By considering spectral triples on S2μ,c(c>0) constructed by Chakraborty and Pal (Commun Math Phys 240(3):447–456, 2000), we show that in general the quantum group of volume and orientation preserving isometries (in the sense of Bhowmick and Goswami in J Funct Anal 257:2530–2572, 2009) for a spectral triple of compact type may not have a C*-action, and moreover, it can fail to be a matrix quantum group. It is also proved that the category with objects consisting of those volume and orientation preserving quantum isometries which induce C*-action on the C* algebra underlying the given spectral triple, may not have a universal object.

Item Type:Article
Source:Copyright of this article belongs to Springer Verlag.
Keywords:Spectral Triples; Compact Quantum Groups; Quantum Isometry Groups; Quantum Spheres
ID Code:102166
Deposited On:01 Feb 2018 04:02
Last Modified:01 Feb 2018 04:02

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