2006/08/29 by Alexander Zimmermann, Zimmermann, Alexander
Mathematics · #16E40 #17B50 #18E30 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16E40 #msc:17B50 #msc:18E30
paper · pdf · doi:10.48550/arxiv.math/0608712
arxiv created 2006/08/29 · arxiv updated 2009/12/01
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.