Classification of low-dimensional real Lie algebras

This mathematics-related list provides Mubarakzyanov's classification of low-dimensional real Lie algebras, published in Russian in 1963.

[1] It complements the article on Lie algebra in the area of abstract algebra.

An English version and review of this classification was published by Popovych et al.[2] in 2003.

Let

g

n

{\displaystyle {\mathfrak {g}}_{n}}

-dimensional Lie algebra over the field of real numbers with generators

[clarification needed] For each algebra

we adduce only non-zero commutators between basis elements.

Algebra

can be considered as an extreme case of

β → ∞

, forming contraction of Lie algebra.

Over the field

algebras

are isomorphic to

Algebra

can be considered as an extreme case of

β → 0

, forming contraction of Lie algebra.

Over the field

algebras

are isomorphic to