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arXiv · 1205.6058

Homotopy unital A_infinity-algebras

Volodymyr Lyubashenko
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Abstract

It is well known that the differential graded operad of A_infinity-algebras is a cofibrant replacement (a dg-resolution) of the operad of associative differential graded algebras without units. In this article we find a cofibrant replacement of the operad of associative differential graded algebras with units. Algebras over it are called homotopy unital A_infinity-algebras. We prove that the operad bimodule of A_infinity-morphisms is a cofibrant replacement of the operad bimodule of morphisms of dg-algebras without units. Similarly we show that the operad bimodule of homotopy unital A_infinity-morphisms is a cofibrant replacement of the operad bimodule of morphisms of dg-algebras with units.

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BibTeXRIS

Volodymyr Lyubashenko. 2012-05-28. Homotopy unital A_infinity-algebras. https://doi.org/10.1016/j.jalgebra.2010.02.009

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