Guin, SatyajitSatyajitGuinSaurabh, BipulBipulSaurabh2025-08-312025-08-312022-09-0110.1007/s11040-022-09432-72-s2.0-85136800712https://d8.irins.org/handle/IITG2025/25947In this article, we study homogeneous spaces U<inf>q</inf>(2) / <inf>ϕ</inf>T and U<inf>q</inf>(2) / <inf>ψ</inf>T of the compact quantum group Uq(2),q∈C\{0}. The homogeneous space U<inf>q</inf>(2) / <inf>ϕ</inf>T is shown to be the braided quantum group SU<inf>q</inf>(2). The homogeneous space U<inf>q</inf>(2) / <inf>ψ</inf>T is established as a universal C^∗-algebra given by a finite set of generators and relations. Its K-groups are computed and two families of finitely summable odd spectral triples, one is U<inf>q</inf>(2) -equivariant and the other is T²-equivariant, are constructed. Using the index pairing, it is shown that the induced Fredholm modules for these families of spectral triples give each element in the K-homology group K¹(C(U<inf>q</inf>(2) / <inf>ψ</inf>T)).falseGNS space | Homogeneous extension | Quantum unitary group | Spectral triplesArticle15729656September 2022321arJournal2WOS:000837675500001