Lie algebras MOC
While the Lie algebra was first invoked to study the Lie group, they are an interesting object in their own right. See also the more general Algebra theory MOC.
Objects
Additional structure
Special constructions of Lie algebras
- Associated Lie algebra of a positive definite even lattice
- Affine Lie algebra
- Twisted affine Lie algebra
Types of Lie algebra
- Simple Lie algebra
- Abelian Lie algebra
- Solvable Lie algebra
- Nilpotent Lie algebra
- Heisenberg algebra
- Triangular Lie algebra
Special Lie algebras
Subalgebras
Morphisms
- Lie algebra homomorphism, Lie algebra isomorphism, Lie algebra automorphism
- Kernel of a Lie algebra homomorphism
Internally
- Lie algebra ideal
- Centralizer in a Lie algebra
- Normalizer in a Lie algebra
- Centre of a Lie algebra
- Radical of a Lie algebra
Externally
- Quotient Lie algebra
- Lie algebra extension
- Direct product of Lie algebras
- Semidirect product of Lie algebras
Representations
- Lie algebra representation, Module over a Lie algebra
- Adjoint Lie algebra representation
- Sum of commuting Lie algebra representations
- Tensor product of Lie algebra representations
Other things
#MOC | #state/tidy | #lang/en | #SemBr