Formal deformations, cohomology theory and L∞[1]-structures for differential Lie algebras of arbitrary weight

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-08-30 DOI:10.1016/j.geomphys.2024.105308

Weiguo Lyu , Zihao Qi , Jian Yang , Guodong Zhou

引用次数: 0

Abstract

We introduced a cohomology theory for differential Lie algebras of arbitrary weight which generalised a previous work of Jiang and Sheng. The underlying $L_{\infty} [1]$ -structure on the cochain complex is also determined via a generalised version of higher derived brackets. The equivalence between $L_{\infty} [1]$ -structures for absolute and relative differential Lie algebras is established. Formal deformations and abelian extensions are interpreted by using lower degree cohomology groups. Also we introduce the homotopy differential Lie algebras.

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任意权重微分列阵的形式变形、同调理论和 L∞[1] 结构

我们引入了任意权重微分李代数的同调理论，该理论概括了蒋和盛的前人工作。共链复数上的基本 L∞[1]- 结构也是通过广义版的高导出括号确定的。建立了绝对微分和相对微分李代数的 L∞[1]- 结构之间的等价性。通过使用低度同调群来解释形式变形和无性扩展。此外，我们还介绍了同调微分李代数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity