The representation-type characterization of Property PC

A restricted Lie algebra is a Lie algebra over a field $k$ equipped with a compatible $p$-operation; its representation type is finite, tame, or wild according to the classification of its finite-dimensional representations. Property PC is the tensor-triangular and support-theoretic property defined in the paper for restricted Lie algebras.

Property PC conjecture. For any restricted Lie algebra ${\mathfrak g}$ over $k$, ${\mathfrak g}$ satisfies Property PC if and only if ${\mathfrak g}$ is of tame or finite representation type.

The paper proves that no abelian restricted Lie algebra of wild representation type satisfies Property PC and gives finite- and tame-type examples, motivating the proposed characterization; the general converse and the full equivalence remain open.