Deformation of L∞-Algebras
نویسنده
چکیده
In this paper, deformations of L∞-algebras are defined in such a way that the bases of deformations are L∞-algebras, as well. A universal and a semiuniversal deformation is constructed for L∞-algebras, whose cotangent complex admits a splitting. The paper also contains an explicit construction of a minimal L∞-structure on the homology H of a differential graded Lie algebra L and of an L∞-quasi-isomorphism between H and L.
منابع مشابه
Arithmetic Deformation Theory of Lie Algebras
This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...
متن کاملDeformation of Singularities via L∞-Algebras
This is an addendum to the paper “Deformation of L∞-Algebras” [9]. We explain in which way the deformation theory of L∞-algebras extends the deformation theory of singularities. We show that the construction of semi-universal deformations of L∞-algebras gives explicit formal semiuniversal deformations of isolated singularities. Introduction In this paper, we apply the following general idea for...
متن کامل∞ - Algebras , Cartan Homotopies and Period Maps
We prove that, for every compact Kähler manifold, the period map of its Kuranishi family is induced by a natural L∞-morphism. This implies, by standard facts about L∞-algebras, that the period map is a “morphism of deformation theories” and then commutes with all deformation theoretic constructions (e.g. obstructions).
متن کاملSemicosimplicial Dglas in Deformation Theory
We describe a canonical L∞ structure on the total complex of a semicosimplicial differential graded Lie algebra and give an explicit descriprion of the Maurer-Cartan elements and of the associated deformation functor in the particular case of semicosimplicial Lie algebras. We use these results to investigate the deformation functor associated to a sheaf of Lie algebras L and to show that it is ...
متن کاملConstruction of Miniversal Deformations of Lie Algebras
In this paper we consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. By “deformations of a Lie algebra” we mean the (affine algebraic) manifold of all Lie brackets. Consider the quotient of this variety by the action of the group GL. It is well-known (see [Hart]) that in the category of algebraic varieties the quotient by a group action does no...
متن کامل