We show that the restricted Lie algebra structure on Hochschild cohomology is
invariant under stable equivalences of Morita type between self-injective
algebras. Thereby we obtain a number of positive characteristic stable
invariants, such as the p-toral rank of HH1(A,A). We also prove a
more general result concerning Iwanaga Gorenstein algebras, using a more
general notion of stable equivalences of Morita type. We provide several
applications to commutative algebra and modular representation theory. The
proof exploits in an essential way the Bββ-structure of the Hochschild
cochain complex. In the appendix we explain how the well-definedness of the
p-power operation on Hochschild cohomology follows from some (originally
topological) results of May and Cohen, and (on the algebraic side) Turchin. We
give complete proofs, using the language of operads.Comment: 20 pages, v2: inaccurate statement about restriction functors
correcte