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Zbl 0894.18008
Hinich, Vladimir
Homological algebra of homotopy algebras. (English)
[J] Commun. Algebra 25, No.10, 3291-3323 (1997). ISSN 0092-7872; ISSN 1532-4125/e

If $k$ is a ring and $C(k)$ the category of unbounded complexes of $k$-modules, then there is a well structured homological (in fact homotopical) algebra defined on $C(k)$. Replacing $k$ by a d.g. algebra, the same result holds. This possibility of working with unbounded complexes is important if one wants to go beyond d.g. algebras to weak algebras in which associativity, etc. hold only up to higher homotopies. A convenient setting then is that of operads and operad algebras and in this paper the author shows that the usual theory extends with great simplicity to that very much more general setting. This enables the definition of cohomology of operad algebras and a corresponding cotangent complex to be defined.
[T.Porter (Bangor)]

MSC 2000:: *18G55 Nonabelian homotopical algebra
18G25 Relative homological algebra
18C15 Triples

Keywords: tangent Lie algebra; homotopical algebra; operads; operad algebras

Cited in: Zbl 1260.18001 Zbl 1228.18006 Zbl 1227.18007 Zbl 1041.18011 Zbl 1020.18007

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