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Mat. Zametki, 2017, Volume 102, Issue 6, Pages 874–895 (Mi mz11301)  

This article is cited in 1 scientific paper (total in 1 paper)

Cyclic Modules with $\infty$-Simplicial Faces and the Cyclic Homology of $A_\infty$-Algebras

S. V. Lapin

Saransk

Abstract: A chain bicomplex for $A_\infty$-algebras, which generalizes the Tsygan chain bicomplex in the theory of cyclic homology of associative algebras, is constructed by using the techniques of differential modules with $\infty$-simplicial faces and $D_\infty$-differential modules. For homotopy unital $A_\infty$-algebras, an exact sequence generalizing the Connes–Tsygan exact sequence for unital associative algebras is obtained.

Keywords: cyclic homology, $A_\infty$-algebra, cyclic simplicial module, differential module with $\infty$-simplicial faces, $D_\infty$-differential module.

DOI: https://doi.org/10.4213/mzm11301

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English version:
Mathematical Notes, 2017, 102:6, 806–823

Bibliographic databases:

Document Type: Article
UDC: 515.14
Received: 28.06.2016
Revised: 17.04.2017

Citation: S. V. Lapin, “Cyclic Modules with $\infty$-Simplicial Faces and the Cyclic Homology of $A_\infty$-Algebras”, Mat. Zametki, 102:6 (2017), 874–895; Math. Notes, 102:6 (2017), 806–823

Citation in format AMSBIB
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\by S.~V.~Lapin
\paper Cyclic Modules with~$\infty$-Simplicial Faces and the Cyclic Homology of $A_\infty$-Algebras
\jour Mat. Zametki
\yr 2017
\vol 102
\issue 6
\pages 874--895
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\crossref{https://doi.org/10.4213/mzm11301}
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\transl
\jour Math. Notes
\yr 2017
\vol 102
\issue 6
\pages 806--823
\crossref{https://doi.org/10.1134/S0001434617110219}
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  • https://doi.org/10.4213/mzm11301
  • http://mi.mathnet.ru/eng/mz/v102/i6/p874

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Lapin V S., “Cyclic Homology of Cyclic Infinity-Simplicial Modules”, Georgian Math. J., 25:4 (2018), 571–591  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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