Hopf coactions on odd spheres.

We prove that the q-deformed unitary group, i.e., U q (N) , is the universal compact quantum group in the category of (compact) quantum groups which coact on the q-deformed odd sphere S q 2 N − 1 leaving the space spanned by the natural set of generators invariant and preserving the unique S U q (N) invariant functional on S q 2 N − 1. Using this, we identify U q (N) as the quantum group of orientation preserving isometries (in the sense of Bhowmick and Goswami [5]) for a natural spectral triple associated with S q 2 N − 1 constructed by Chakraborty and Pal [9]. [ABSTRACT FROM AUTHOR]