Lie algebra
vector space with an alternating binary operation satisfying the Jacobi identity.
compact Lie algebra
mathematical theory
Lie ring
ring that forms a Lie algebra under multiplication
linear Lie algebra
Lie subalgebra of the general linear group
modular Lie algebra
Lie algebra over a field of positive characteristic
reductive Lie algebra
in mathematics, a Lie algebra whose adjoint representation is completely reducible
split Lie algebra
Lie algebra equipped with a splitting Cartan subalgebra
quadratic Lie algebra
Lie algebra equipped with a compatible quadratic form
Poisson algebra
associative algebra together with a Lie bracket that also satisfies Leibniz's law
free Lie algebra
free object in the category of Lie algebras
general linear Lie algebra
Lie algebra of endomorphisms of a vector space; Lie algebra corresponding to the general linear group
Witt algebra
one of basic infinite-dimensional Lie algebras
affine Lie algebra
type of Kac–Moody algebras
solvable Lie algebra
Lie algebra whose derived series terminates in the zero subalgebra
graded Lie algebra
Lie algebra equipped with a grading compatible with the Lie bracket