The universal Property PB conjecture for restricted Lie algebras

Let ${\mathfrak g}$ be a restricted Lie algebra over a field $k$. Property PB is the weaker support-theoretic property defined in the paper for restricted Lie algebras and their representation categories.

Property PB conjecture. All restricted Lie algebras satisfy Property PB regardless of representation type.

The conjecture asserts Property PB even for wild representation type, in contrast with the proposed representation-type characterization of Property PC. The paper indicates that this is a further conjecture and that proving related results may require classification of cocommutative Hopf algebra structures beyond what is currently known.