Cosimplicial DGLAs in Deformation Theory
نویسندگان
چکیده
منابع مشابه
Semicosimplicial 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 کاملHochschild Dglas and Torsion Algebras
The associator of a non-associative algebra is the curvature of the Hochschild quasi-complex. The relationship “curvature-associator” is investigated. Based on this generic example, we extend the geometric language of vector fields to a purely algebraic setting, similar to the context of Gerstenhaber algebras. We interprete the elements of a non-associative algebra with a Lie bracket as “vector...
متن کاملDeformation Theory
In mathematical deformation theory one studies how an object in a certain category of spaces can be varied in dependence of the points of a parameter space. In other words, deformation theory thus deals with the structure of families of objects like varieties, singularities, vector bundles, coherent sheaves, algebras or differentiable maps. Deformation problems appear in various areas of mathem...
متن کاملDeformation Theory
In these notes we’ll give an introduction to deformation theory and apply it to the special case of abelian schemes. We’ll start by defining the deformation functor and show how the cohomology groups of the sheaf of derivations of a scheme can be used to both determine if deformations exist and if so, what the set of deformations looks like. After that, we’ll introduce the 800 pound gorilla of ...
متن کاملDeformation Theory
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section 6 we generalize the Maurer-Cartan equation to strongly homotopy Li...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2012
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2011.577479