Fine Hochschild invariants of derived categories for symmetric algebras

Details Fine Hochschild invariants of derived categories for symmetric algebras Fine Hochschild invariants of derived categories for symmetric algebras

2006-08-29

arxiv.org/abs/math/0608712v1

Mathematics

Representation Theory

Scientific paper

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.

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