Fine Hochschild invariants of derived categories for symmetric algebras
A. Zimmermann.

Abstract:
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.