Quantum subgroups of GLα,β(n)

AbstractLet α,β∈C∖{0} and ℓ∈N be odd with ℓ⩾3. We determine all Hopf algebra quotients of the quantized coordinate algebra Oα,β(GLn) when α−1β is a primitive ℓ-th root of unity and α, β satisfy certain mild conditions, and we characterize all finite-dimensional quotients when α−1β is not a root of unity. As a byproduct we find a new family of non-semisimple and non-pointed Hopf algebras with non-pointed duals which are quotients of Oα,β(GLn)