Homotopy algebras via resolutions of operads

Markl, Martin

Displaying similar documents to “Homotopy algebras via resolutions of operads”

Homotopy diagrams of algebras

Markl, Martin

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The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [ and , Homotopy invariant algebraic structures on topological spaces, Lect. Notes Math. 347, Springer-Verlag (1973; Zbl 0285.55012)] from topology to algebra.In topology the notion of operad extracts the essential algebraic information contained in the following example (endomorphism operad).The endomorphism operad $ℰ_{X}$ of a based space $X$ consists of the family...

Derivations of homotopy algebras

Tom Lada, Melissa Tolley (2013)

Archivum Mathematicum

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We recall the definition of strong homotopy derivations of $A_{\infty}$ algebras and introduce the corresponding definition for $L_{\infty}$ algebras. We define strong homotopy inner derivations for both algebras and exhibit explicit examples of both.

The Milnor-Moore theorem in Tame Homotopy theory.

Hans Scheerer, Daniel Tanré (1991)

Manuscripta mathematica

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On the cohomology algebra of a fiber.

Menichi, Luc (2001)

Algebraic & Geometric Topology

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On the adjoint map of homotopy abelian DG-Lie algebras

Donatella Iacono, Marco Manetti (2019)

Archivum Mathematicum

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We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.