Titlebook: Lie Methods in Deformation Theory; Marco Manetti Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Spr

Obscure

-Algebras,rmation functors to them. It is easy to give the definition of .-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.

vibrant

Coalgebras and Coderivations,understand. One of the goals of this chapter is to reinterpret both the Nijenhuis–Richardson bracket and the category of formal neighbourhoods in the framework of graded coalgebras. This will allow us to give, in Chap. 12, a useful equivalent characterization of . structures which leads naturally to

出价

libertine

Formal Kuranishi Families and Period Maps,theory. The first two sections of this chapter are devoted to the proof that every .-morphism induces natural transformations of both Maurer–Cartan and deformation functors, together with an interpretation of the formal Kuranishi family in terms of homotopy transfer of . structure.

encomiast

Tree Summation Formulas,In this chapter we consider the cases where the combinatorial data involved are rooted trees (Definition 14.1.2) possibly equipped with additional data (orientation, labelling etc.). In particular, we shall provide tree summation formulas for the BCH product (recursive formula of Definition 2.5.1) a

联合

https://doi.org/10.1007/978-981-19-1185-9deformation theory; differential graded Lie algebras; L-infinity algebras; simplicial methods; Deligne g

Recess

Lie Algebras,In this chapter, after a brief review of Lie algebras and descending central series, we study free Lie algebras over fields of characteristic 0 and the Baker–Campbell–Hausdorff (BCH) product.

Clinch

,Deformations of Complex Manifolds and Holomorphic Maps,In this chapter we work over the field of complex numbers . and we study deformations of complex manifolds and holomorphic maps from the point of view of DG-Lie algebras.

CUMB

,Poisson, Gerstenhaber and Batalin–Vilkovisky Algebras,In several interesting deformation problems the controlling differential graded Lie algebra admits an enhanced algebraic structure, and this is usually useful in the study of its homotopy type and of its associated deformation functor.

渗入

978-981-19-1187-3The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor