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Spectral sequences for Hochschild cohomology and graded centers of derived categories

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Abstract

The Hochschild cohomology of a differential graded algebra, or a differential graded category, admits a natural map to the graded center of its homology category: the characteristic homomorphism. We interpret it as an edge homomorphism in a spectral sequence. This gives a conceptual explanation of the failure of the characteristic homomorphism to be injective or surjective, in general. To illustrate this, we discuss modules over the dual numbers, coherent sheaves over algebraic curves, as well as examples related to free loop spaces and string topology.

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Authors and Affiliations

  1. Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK

    Frank Neumann

  2. Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Markus Szymik

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  1. Frank Neumann
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  2. Markus Szymik
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Correspondence to Markus Szymik.

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Neumann, F., Szymik, M. Spectral sequences for Hochschild cohomology and graded centers of derived categories. Sel. Math. New Ser. 23, 1997–2018 (2017). https://doi.org/10.1007/s00029-017-0331-9

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