Fine Hochschild invariants of derived categories for symmetric algebras

Abstract

Let $A$ be a symmetric $k$-algebra over a perfect field $k$. Külshammer defined for any integer $n$ a mapping $ζ\_n$ on the degree 0 Hochschild cohomology and a mapping $κ\_n$ 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 $ζ\_n$ is invariant under derived equivalences. In the present paper we generalize the definition of $κ\_n$ to higher Hochschild homology and show the invariance of $κ$ and its generalization under derived equivalences. This provides fine invariants of derived categories.