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. 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. in 2003. Mubarakzyanov's Classification. Let formula_1 be formula_2-dimensional Lie algebra over the field of real numbers with generators formula_3, formula_4. For each algebra formula_5 we adduce only non-zero commutators between basis elements. Algebra formula_18 can be considered as an extreme case of formula_24, when  formula_34, forming contraction of Lie algebra. Three-dimensional. Over the field formula_35 algebras formula_24, formula_29 are isomorphic to formula_38 and formula_26, respectively. Four-dimensional. Algebra formula_79 can be considered as an extreme case of formula_80, when formula_81, forming contraction of Lie algebra. Over the field formula_35 algebras formula_53, formula_57, formula_85, formula_86, formula_87 are isomorphic to formula_51, formula_55, formula_90, formula_91, formula_92, respectively.