Title: On a class of noetherian prime Hopf algebras

Abstract: Brown and Goodearl proposed a conjecture stating that every prime noetherian Hopf algebra is Auslander Gorenstein (AG). We prove that if a prime noetherian Hopf $k$-algebra is AG, or more generally, if it possesses an Auslander dualizing complex, then it exhibits the bounded factorization property.

We also introduce a non-commutative Poisson Hopf algebra as an ongoing joint work with Ken Brown and James Zhang. Using flat deformation, we provide a recipe that gives us a source of examples. However, it remains uncertain whether there are examples not derived from this recipe.