This article is cited in 5 papers

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.

UDC: 515.14

Received: 28.06.2016
Revised: 17.04.2017

DOI: 10.4213/mzm11301

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

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