On the Lie algebra structure of integrable derivations

Abstract Building on work of Gerstenhaber, we show that the space integrable derivations an Artin algebra forms a Lie algebra, and restricted if contains field characteristic . We deduce classes in (restricted) is invariant under derived equivalences, stable equivalences Morita type between self‐injective algebras. also provide negative answers to questions about posed by Linckelmann Farkas, Geiss Marcos. Along way, compute first Hochschild cohomology group any symmetric group.