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