关于李括号、交叉模和李-莱因哈特代数的历史

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2022-08-04 DOI:10.3934/jgm.2021009

J. Huebschmann

引用次数: 3

摘要

本文概述了早期同伦理论中的括号、交叉模、非阿贝可拓问题的阻塞3环、Teichmuller环、Lie- rinehart代数、Lie代数群和微分代数。

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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On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras

This is an overview of ideas related to brackets in early homotopy theory, crossed modules, the obstruction 3-cocycle for the nonabelian extension problem, the Teichmuller cocycle, Lie-Rinehart algebras, Lie algebroids, and differential algebra.

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来源期刊

Journal of Geometric Mechanics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal: 1. Lagrangian and Hamiltonian mechanics 2. Symplectic and Poisson geometry and their applications to mechanics 3. Geometric and optimal control theory 4. Geometric and variational integration 5. Geometry of stochastic systems 6. Geometric methods in dynamical systems 7. Continuum mechanics 8. Classical field theory 9. Fluid mechanics 10. Infinite-dimensional dynamical systems 11. Quantum mechanics and quantum information theory 12. Applications in physics, technology, engineering and the biological sciences.