Engineering↗
Definition of Lie Algebra Cohomology
Lie algebra cohomology as Ext over the enveloping algebra, invariants and coinvariants, the explicit description in degrees 0 and 1, and derivations.
Tag
Cohomology of Lie Algebras
Every page in the KEVOS library tagged Cohomology of Lie Algebras. 6 pages.
Engineering↗
Hilbert's Syzygy Theorem
Hilbert's chain-of-syzygies theorem, the Koszul resolution, global dimension of polynomial rings, and the historical and modern significance.
Engineering↗
Lie Algebra Extensions and H2
Extensions of Lie algebras with abelian kernel, the classification by H^2, central extensions, and examples including the Heisenberg and affine algebras.
Engineering↗
Lie Algebras and the Universal Enveloping Algebra
Lie algebras, representations as modules, the universal enveloping algebra and its universal property, the Poincare-Birkhoff-Witt theorem, and the augmentation ideal.
Engineering↗
Semisimple Lie Algebras and the Whitehead Lemmas
The Killing form and Cartan's criterion, the Casimir element, the two Whitehead lemmas, and their consequences including Weyl's complete reducibility theorem and Levi's theorem.
Engineering↗
The Chevalley–Eilenberg Resolution
The Chevalley-Eilenberg resolution of the trivial module, its differential, the resulting cochain complex, and the bound on cohomological dimension.
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