: Mathematics: homotopy Lie algebra

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homotopy Lie algebra

In mathematics, in particular abstract algebra and topology, a homotopy Lie algebra (or ${\\displaystyle L_{\\infty }}$ -algebra) is a generalisation of the concept of a differential graded Lie algebra. To be a little more specific, the Jacobi identity only holds up to homotopy. Therefore, a differential graded Lie algebra can be seen as a homotopy Lie algebra where the Jacobi identity holds on the nose. These homotopy algebras are useful in classifying deformation problems over characteristic 0 in deformation theory because deformation functors are classified by quasi-isomorphism classes of L∞-algebras. This was later extended to all characteristics by Jonathan Pridham.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Homotopy_Lie_algebra)

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