Lie algebra cohomology

In mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was first introduced in 1929 by Élie Cartan to study the topology of Lie groups and homogeneous spaces[1] by relating cohomological methods of Georges de Rham to properties of the Lie algebra. It was later extended by Claude Chevalley and Samuel Eilenberg (1948) to coefficients in an arbitrary Lie module.[2]

  1. ^ Cartan, Élie (1929). "Sur les invariants intégraux de certains espaces homogènes clos". Annales de la Société Polonaise de Mathématique. 8: 181–225.
  2. ^ Koszul, Jean-Louis (1950). "Homologie et cohomologie des algèbres de Lie". Bulletin de la Société Mathématique de France. 78: 65–127. doi:10.24033/bsmf.1410. Archived from the original on 2019-04-21. Retrieved 2019-05-03.