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

@article{Huebschmann2022OnTH, title={On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras}, author={Johannes Huebschmann}, journal={Journal of Geometric Mechanics}, year={2022} }

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.

## 2 Citations

### From Lie algebra crossed modules to tensor hierarchies

- MathematicsJournal of Pure and Applied Algebra
- 2022

### A Lie-Rinehart algebra in general relativity

- Mathematics
- 2022

We construct a Lie-Rinehart algebra over an infinitesimal extension of the space of initial value fields for Einstein's equations. The bracket relations in this algebra are precisely those of the…

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