On quantum quaternion spheres

摘要: We give an explicit description of the $q$-deformation symplectic group $SP_{q}(2n)$ at $C^*$-algebra level and find all irreducible representations this $C^{*}$-algebra. Further we describe quotient space $SP_{q}(2n)/SP_{q}(2n-2)$ in terms generators relations. compute its $K$-theory by obtaining a chain short exact sequence for $C^{*}$-algebras underlying such manifolds.