doi: 10.3934/jgm.2021009

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

Université de Lille - Sciences et Technologies, Département de Mathématiques, CNRS-UMR 8524, Labex CEMPI (ANR-11-LABX-0007-01), 59655 Villeneuve d'Ascq Cedex, France

Dedicated to the memory of Kirill Mackenzie

Received  March 2021 Published  May 2021

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 Teichmüller cocycle, Lie-Rinehart algebras, Lie algebroids, and differential algebra.

Citation: Johannes Huebschmann. On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras. Journal of Geometric Mechanics, doi: 10.3934/jgm.2021009
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