Title: Deforming tensor products for restricted representations of Lie algebras.
Abstract: What can the classification of Hopf algebras of small dimension over a field tell us about families of tensor categories? Fixing a finite dimensional algebra, letting a Hopf algebra structure be taken as variable is equivalent under Tannakian duality to letting the k-linear tensor product over the category of modules be variable. Ideally we could describe explicitly how the Green ring is changing, but for algebras of wild representation type this is likely infeasible. It turns out starting with the restricted enveloping algebra for a restricted Lie algebra (characteristic p > 0) allows a nice perspective from tensor-triangular geometry. We will see an example of a tame Lie algebra, with all Hopf algebra structures known up to isomorphism, satisfying a tt-geometry flavored property pertaining to its variable Green ring.