Abstract
We prove that the q-deformed unitary group, i.e., Uq(N), is the universal compact quantum group in the category of (compact) quantum groups which coact on the q-deformed odd sphere Sq2N−1 leaving the space spanned by the natural set of generators invariant and preserving the unique SUq(N) invariant functional on Sq2N−1. Using this, we identify Uq(N) as the quantum group of orientation preserving isometries (in the sense of Bhowmick and Goswami [5]) for a natural spectral triple associated with Sq2N−1 constructed by Chakraborty and Pal [9].
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