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

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

<p style='text-indent:20px;'>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.</p>