  Building on work of Gerstenhaber, we show that the space of integrable
derivations on an Artin algebra $A$ forms a Lie algebra, and a restricted Lie
algebra if $A$ contains a field of characteristic $p$. We deduce that the space
of integrable classes in $\HH^1(A)$ forms a (restricted) Lie algebra that is
invariant under derived equivalences, and under stable equivalences of Morita
type between self-injective algebras. We also provide negative answers to
questions about integrable derivations posed by Linckelmann and by Farkas,
Geiss and Marcos.
