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We show that Nichols algebras of most simple Yetter–Drinfeld modules over the projective special linear group over a finite field, corresponding to non-semisimple orbits, have infinite dimension. We spell out a new criterium to show that a rack collapses.
Let 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...
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