# On the Lie algebra structure of integrable derivations

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.