Differential modules with $\infty$-simplicial faces and $A_\infty$-algebras
Abstract
In the present paper, by using the colored version of the Koszul duality, the concept of a differential module with -simplicial faces is introduced. The homotopy invariance of the structure of a differential module with -simplicial faces is proved. The relationships between differential modules with -simplicial faces and -algebras are established. The notion of a chain realization of a differential module with -simplicial faces and the concept of a tensor product of differential modules with -simplicial faces are introduced. It is proved that for an arbitrary -algebra the chain realization of the tensor differential module with -simplicial faces, which corresponds to this -algebra, and the -construction of this -algebra are isomorphic differential coalgebras.
Keywords
Cite
@article{arxiv.1809.01853,
title = {Differential modules with $\infty$-simplicial faces and $A_\infty$-algebras},
author = {S. V. Lapin},
journal= {arXiv preprint arXiv:1809.01853},
year = {2018}
}