Geodesic
Cyclic Modules with~$\infty$-Simplicial Faces and the Cyclic Homology of $A_\infty$-Algebras
Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 874-895

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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. 
@article{MZM_2017_102_6_a8,
     author = {S. V. Lapin},
     title = {Cyclic {Modules} with~$\infty${-Simplicial} {Faces} and the {Cyclic} {Homology} of $A_\infty${-Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {874--895},
     publisher = {mathdoc},
     volume = {102},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a8/}
}
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S. V. Lapin. Cyclic Modules with~$\infty$-Simplicial Faces and the Cyclic Homology of $A_\infty$-Algebras. Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 874-895. http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a8/