Brown–Goodearl conjecture on AS-Gorenstein Hopf algebras

Prove that every noetherian Hopf algebra is Artin–Schelter Gorenstein.

Background

The paper reviews Artin–Schelter Gorenstein Hopf algebras and homological integrals. It notes that noetherian affine PI Hopf algebras are known to be Artin–Schelter Gorenstein, but that the corresponding assertion for arbitrary noetherian Hopf algebras is formulated as the Brown–Goodearl conjecture. Establishing this conjecture would extend the known result beyond the affine PI setting and provide a general homological finiteness property for noetherian Hopf algebras.

References

Now the Brown-Goodearl conjecture asserts that every noetherian Hopf algebra is AS-Gorenstein.

— Homological properties of quantum groups governed by small quantum groups  (2609.08205 - Huang et al., 8 Sep 2026) in Section 2, Subsection 2.1, immediately following the discussion of noetherian affine PI Hopf algebras