Hopf coactions on odd spheres

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 S 2N−1 q leaving the space spanned by the natural set of generators invariant and preserving the unique SUq(N ) invariant functional on S 2N−1 q . Using this, we identify Uq(N ) as the quantum group of orientation preserving isometries (in the sense of Bhowmick and Goswami [BG09]) for a natural spectral triple associated with S 2N−1 q constructed by Chakraborty and Pal [CP08].