Abstract
On the basis of the colored version of Koszul duality, the notion of a differential module with ∞-simplicial faces is introduced. By using the homotopy technique of differential Lie modules over colored coalgebras, the homotopy invariance of the structure of a differential module with ∞-simplicial faces is proved. A relationship between differential modules with ∞-simplicial faces and A ∞-algebras is described. The notions of the chain realization of a differential module with ∞-simplicial faces and the tensor product of differential modules with ∞-simplicial faces are introduced. It is shown that the chain realization of a tensor differential module with ∞-simplicial faces constructed from an A ∞-algebra and the B-construction over this A ∞-algebra are isomorphic differential coalgebras.
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Original Russian Text © S. V. Lapin, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 1, pp. 101–124.
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Lapin, S.V. Chain realization of differential modules with ∞-simplicial faces and the B-construction over A ∞-algebras. Math Notes 98, 111–129 (2015). https://doi.org/10.1134/S000143461507010X
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DOI: https://doi.org/10.1134/S000143461507010X