Abstract
The aim of this chapter is to present \(L_{\infty }\)-algebras as a natural generalization of differential graded Lie algebras, and to extend Maurer–Cartan and deformation functors to them. It is easy to give the definition of \(L_{\infty }\)-algebras; it is sufficient to modify the notion of a differential graded Lie algebra by imposing that the Jacobi identity holds only up to a hierarchy of higher homotopies.
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Notes
- 1.
We shall prove later (Lemma 13.1.3) that homotopy equivalence is already an equivalence relation.
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Manetti, M. (2022). \(L_{\infty }\)-Algebras. In: Lie Methods in Deformation Theory. Springer Monographs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1185-9_10
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DOI: https://doi.org/10.1007/978-981-19-1185-9_10
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Online ISBN: 978-981-19-1185-9
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