O A ] 3 O ct 2 00 8 Quantum isometry groups of the Podles Spheres by

For μ ∈ [0, 1], c > 0, We identify the quantum group SOμ(3) as the universal object in the category of compact quantum groups acting ‘by orientation and volume preserving isometries’ in the sense of [8] on the natural spectral triple on the Podles sphere S μc constructed by Dabrowski, D’Andrea, Landi and Wagner in [16]. Moreover, we explicitly compute such universal quantum groups for another class of spectral triples on S μ,c constructed by Chakraborty and Pal ([11]).

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