Stable invariance of the restricted Lie algebra structure of Hochschild cohomology

On the Lie algebra structure of integrable derivations

“…In positive characteristic this respects the $$p$$‐power structure by [15, (3.2)] combined with [5, Theorem 2]. For the case of self‐injective algebras that are stably equivalent of Morita type, there is by [18, Theorem 5.1] an isomorphism $${\operatorname{HH}}_{\rm int}^1(A)\cong {\operatorname{HH}}_{\rm int}^1(B)$$ induced by a transfer map, and this is an isomorphism of restricted Lie algebras by Corollary 1 together with [26, Theorem 1.1] and [5, Theorem 1].$$\Box$$…”

“…For the case of self-injective algebras that are stably equivalent of Morita type, there is by [18, Theorem 5.1] an isomorphism HH 1 int (𝐴) ≅ HH 1 int (𝐵) induced by a transfer map, and this is an isomorphism of restricted Lie algebras by Corollary 1 together with [26, Theorem 1.1] and [5,Theorem 1]. □…”