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An interpretation of E n -homology as functor homology

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Abstract

We prove that E n -homology of non-unital commutative algebras can be described as functor homology when one considers functors from a certain category of planar trees with n levels. For different n these homology theories are connected by natural maps, ranging from Hochschild homology and its higher order versions to Gamma homology.

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Authors and Affiliations

  1. Université Paris 13, CNRS, UMR 7539 LAGA, 99 avenue Jean-Baptiste Clément, 93430, Villetaneuse, France

    Muriel Livernet

  2. Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Birgit Richter

Authors
  1. Muriel Livernet
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  2. Birgit Richter
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Correspondence to Birgit Richter.

Additional information

M. Livernet thanks MIT and the Clay Institute for hosting her and Haynes Miller for conversations on E n -algebras. B. Richter thanks the Institut Galilée of Université Paris 13 for an invitation as professeur invité that led to this work. We are grateful to Benoit Fresse for catching a serious sign error and to Aurélien Djament for suggesting a different setting for our proof of proposition 4.4. We thank the referee for his/her careful reading of the paper.

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Livernet, M., Richter, B. An interpretation of E n -homology as functor homology. Math. Z. 269, 193–219 (2011). https://doi.org/10.1007/s00209-010-0722-5

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  • DOI: https://doi.org/10.1007/s00209-010-0722-5

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