Hopf coactions on odd spheres

2018/08/27 by Bhattacharjee, Suvrajit, Goswami, Debashish
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1808.08698

Abstract

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^2N-1 leaving the space spanned by the natural set of generators invariant and preserving the unique SU_q(N) invariant functional on S_q^2N-1. Using this, we identify U_q(N) as the quantum group of orientation preserving isometries (in the sense of Bhowmick and Goswami \citeMR2555012) for a natural spectral triple associated with S_q^2N-1 constructed by Chakraborty and Pal \citeMR2458039.

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• Quantum Group of Orientation preserving Riemannian Isometries
• Twisting the q-deformations of compact semisimple Lie groups
• Characterization of SU_q(ℓ+1)-equivariant spectral triples for the odd dimensional quantum spheres
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