  Let $A$ be a symmetric $k$-algebra over a perfect field $k$. K\"ulshammer
defined for any integer $n$ a mapping $\zeta\_n$ on the degree 0 Hochschild
cohomology and a mapping $\kappa\_n$ on the degree 0 Hochschild homology of $A$
as adjoint mappings of the respective $p$-power mappings with respect to the
symmetrizing bilinear form. In an earlier paper it is shown that $\zeta\_n$ is
invariant under derived equivalences. In the present paper we generalize the
definition of $\kappa\_n$ to higher Hochschild homology and show the invariance
of $\kappa$ and its generalization under derived equivalences. This provides
fine invariants of derived categories.
