Fine Hochschild invariants of derived categories for symmetric algebras

Let A be a symmetric k-algebra over a perfect field k. Külshammer defined for any integer n a mapping ζn on the degree 0 Hochschild cohomology and a mapping κn on the degree 0 Hochschild homology of A as adjoint mappings of the respective p-power mappings with respect to the symmetrising bilinear form. In an earlier paper it is shown that ζn is invariant under derived equivalences. In the present paper we generalise the definition of κn to higher Hochschild homology and show the invariance of κ and its generalisation under derived equivalences. This provides fine invariants of derived categories.