solvable Lie algebras are analogs of solvable groups. Any nilpotent Lie algebra is a fortiori solvable but the converse is not true. The solvable Lie...

of Lie groups. Analogously to abelian, nilpotent, and solvable groups, one can define abelian, nilpotent, and solvable Lie algebras. A Lie algebra g {\displaystyle...

Lie group should be done for all.[clarification needed] The intersection of reductive Lie algebras and solvable Lie algebras is exactly abelian Lie algebras...

subalgebra of a finite dimensional solvable Lie algebra over a field of characteristic 0 is nilpotent. Solvable Lie algebra Knapp 2002 Proposition 1.32. Serre...

both solvable and semisimple. Semisimple Lie algebras have a very elegant classification, in stark contrast to solvable Lie algebras. Semisimple Lie algebras...

states that any finite-dimensional Lie algebra g over a field of characteristic zero is the semidirect product of a solvable ideal and a semisimple subalgebra...

Look up solvable in Wiktionary, the free dictionary. In mathematics, solvable may refer to: Solvable group, a group that can be constructed by compositions...

an abelian Lie algebra, which is a fortiori solvable. A consequence of Lie's theorem is that any finite dimensional solvable Lie algebra over a field...

smooth connected solvable normal subgroup). Every compact connected Lie group has a complexification, which is a complex reductive algebraic group. In fact...

matrix Lie algebra, there is a linear group (matrix Lie group) with this algebra as its Lie algebra. On the other hand, Lie groups with isomorphic Lie algebras...

gives conditions for a Lie algebra in characteristic 0 to be solvable, which implies a related criterion for the Lie algebra to be semisimple. It is...

group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with...

representation of a solvable Lie algebra is simultaneously upper triangularizable, the case of commuting matrices being the abelian Lie algebra case, abelian...

of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms...

deformations of solvable rather than semisimple Lie groups. They are associated to Lie splittings of Lie algebras or local factorisations of Lie groups and...

low-dimensional real Lie algebras, published in Russian in 1963. It complements the article on Lie algebra in the area of abstract algebra. An English version...

a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently and simultaneously discovered them in 1968) is a Lie algebra, usually infinite-dimensional...

Similarly to the Lie group–Lie algebra correspondence, to an algebraic group over a field k {\displaystyle k} is associated a Lie algebra over k {\displaystyle...

In mathematics, a complex Lie algebra is a Lie algebra over the complex numbers. Given a complex Lie algebra g {\displaystyle {\mathfrak {g}}} , its conjugate...

In abstract algebra, an automorphism of a Lie algebra g {\displaystyle {\mathfrak {g}}} is an isomorphism from g {\displaystyle {\mathfrak {g}}} to itself...

decomposition Lie groupoid Lie subgroup Complex Lie group Local Lie group Poisson–Lie group Real Lie groups Simple Lie group Solvable Lie algebra Special linear...

the mathematical field of Lie theory, the radical of a Lie algebra g {\displaystyle {\mathfrak {g}}} is the largest solvable ideal of g . {\displaystyle...

Lie algebras, like Lie groups, have a Levi decomposition into semisimple and solvable parts, with the representation theory of solvable Lie algebras being...

and solvable linear algebraic group G has dimension 1. In fact, this is another way to state the Lie–Kolchin theorem. The result for Lie algebras was...

This (real) Lie algebra has dimension n2 − 1. More information about the structure of this Lie algebra can be found below in § Lie algebra structure. In...

This article gives a table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group...

extended it to solvable ones. Dixmier (1996, chapter 6) describes the Dixmier mapping in detail. Suppose that g is a completely solvable Lie algebra, and f is...

characterization in terms of eigenvectors. Lie's theorem, which shows that any representation of a solvable Lie algebra is simultaneously upper triangularizable...

the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example...

In mathematics, F4 is a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The...