The space of integrable derivations was introduced by Hasse and Schmidt, and has since been used in geometry and commutative algebra. More recently, integrable derivations have been used as a source of invariants in representation theory.
In this talk I will show that the space of integrable classes in the first Hochschild cohomology of a finite dimensional algebra forms a (restricted) Lie algebra that is invariant under derived equivalences, and under stable equivalences of Morita type between self-injective algebras. I will also provide negative answers to questions posed by Linckelmann and by Farkas, Geiss and Marcos regarding integrable derivations. This is joint work with Benjamin Briggs.