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L-infinity operad

Contents

Context

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Higher algebra

Contents

Idea

The L L_\infty-operad is a cofibrant resolution of the Lie operad in the model structure on operads in the category of chain complexes.

Its algebras over an operad are L-infinity algebras.

References

In chain complexes

Discussion as an operad in chain complexes:

Original articles include

Review includes

  • Jeroen Maes, around Def. 5.6.4 of Derived homotopy algebras, PhD thesis 2016 (web)

See also

In spectra

Discussion as an operad in spectra (in stable homotopy theory) is in

based on

  • Michael Ching, Bar constructions for topological operads and the Goodwillie derivatives of the identity, Geom. Topol. , 9:833–933, 2005 (arXiv:math/0501429)

  • Michael Ching, Bar-cobar duality for operads in stable homotopy theory, Journal of Topology, 2012 (arXiv:1009.5034)

Last revised on August 30, 2018 at 02:48:39. See the history of this page for a list of all contributions to it.