arXiv 0803.03992008-03math.QAmath.AG

Semicosimplicial DGLAs in deformation theory

Domenico Fiorenza, Marco Manetti, Elena Martinengo

备注：: Largely rewritten. Abstract modified. 15 pages, Latex, uses xy-pic
发表信息：: Communications in Algebra Vol. 40, 2012, 2243-2260
DOI：: 10.1080/00927872.2011.577479

英文摘要：

We identify Cech cocycles in nonabelian (formal) group cohomology with Maurer-Cartan elements in a suitable L-infinity algebra. Applications to deformation theory are described.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves

We use the Thom-Whitney construction to show that infinitesimal deformations of a coherent sheaf F are controlled by the differential graded Lie algebra of global sections of an acyclic resolution of the sheaf End(E), where E is any locally free resolution of F. In particular, one recovers the well known fact that the tangent space to deformations of F is Ext^1(F,F), and obstructions are contained in Ext^2(F,F). The main tool is the identification of the deformation functor associated with the Thom-Whitney DGLA of a semicosimplicial DGLA whose cohomology is concentrated in nonnegative degrees …

2009-11-19math.AGmath.QA

Deformations of algebroid stacks

In this paper we consider deformations of an algebroid stack on an etale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.

2009-02-02math.DGmath.QA

Graph complexes in deformation quantization

Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich's pro…

2005-09-05math.QA

Deformations of gerbes on smooth manifolds

We identify the 2-groupoid of deformations of a gerbe on a smooth manifold with the Deligne 2-groupoid of a corresponding twist of the DGLA of local Hochschild cochains on infinite jets of smooth functions.

2007-03-17math.DGmath.QA

Deformation and Hochschild Cohomology of Coisotropic Algebras

Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.

2020-09-07math-phmath.MPmath.QA

A combinatorial approach to coefficients in deformation quantization

Graph cocycles for star-products are investigated from the combinatorial point of view, using Connes-Kreimer renormalization techniques. The Hochschild complex, controlling the deformation theory of associative algebras, is the ``Kontsevich representation'' of a DGLA of graphs coming from a pre-Lie algebra structure defined by graph insertions. Properties of the dual of its UEA (an odd parity analog of Connes-Kreimer Hopf algebra), are investigated in order to find solutions of the deformation equation. The solution of the initial value deformation problem, at tree-level, is unique. For linear…

2004-04-21math-phmath.MPmath.QA

更多相关论文收起更多论文

Poisson structures on sets of Maurer-Cartan elements

Given a differential graded Lie algebra (dgla) L satisfying certain conditions, we construct Poisson structures on the gauge orbits of its set of Maurer-Cartan (MC) elements, termed Maurer-Cartan-Poisson (MCP) structures. They associate a compatible Batalin-Vilkovisky algebra to each MC element of L. An MCP structure is shown to exist for a number of dglas associated to commutative Frobenius algebras, deformations of Poisson and symplectic structures, as well as the Chevally-Eilenberg complex. MCP structures yield a notion of hamiltonian flow of MC elements, and also define Lie algebroids on g…

2022-03-04math.DGmath.QAmath.SG