Fine Hochschild invariants of derived categories for symmetric algebras

Alexander Zimmermann (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

Let $A$ be a symmetric $k$-algebra over a perfect field $k$. Külshammer 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.

Mots clés: Hochschild homology; derived equivalences; generalized Reynold's ideals; Kuelshammer ideals; Gerstenhaber structure

Domaines: Théorie des représentations [math.RT]

Alexander Zimmermann. Fine Hochschild invariants of derived categories for symmetric algebras. Journal of Algebra, 2007, 308 (1), pp.350-367. ⟨hal-00090209⟩