Abstract
Let H be a Hopf algebra over a base field. If H has an ℕ-filtration such that the associated graded ring is connected graded noetherian and has enough normal elements, then H is Gorenstein. This gives a partial solution to a question of Brown and Brown-Goodearl. As a consequence, every quotient Hopf algebra of a generic quantized coordinate ring of a connected semisimple Lie group is Auslander-Gorenstein and Cohen-Macaulay. The last statement answers a question of Goodearl-Zhang.
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