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In mathematics, the Bianchi classification provides a list of all real 3-dimensional Lie algebras (up to isomorphism). The classification contains 11 classes, 9 of which contain a single Lie algebra and two of which contain a continuum-sized family of Lie algebras. (Sometimes two of the groups are included in the infinite families, giving 9 instead of 11 classes.) The classification is important in geometry and physics, because the associated Lie groups serve as symmetry groups of 3-dimensional Riemannian manifolds. It is named for Luigi Bianchi, who worked it out in 1898.

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rdf:type	mean of transportation yago:WikicatLieAlgebras yago:WikicatLieGroups yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:Group100031264 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797
rdfs:label	Bianchi classification (en) Classification de Bianchi (fr) ビアンキ分類 (ja) Классификация Бьянки (ru) 比安基分类 (zh)
rdfs:comment	La classification de Bianchi est une classification des algèbres de Lie réelles de dimension 3, donnée par Luigi Bianchi. (fr) 数学では、(Luigi Bianchi)の名前に因んだ、ビアンキ分類(Bianchi classification)は、リー代数の分類である。 3-次元実リー代数は、11個のクラスに分類され、その中の 9個は単独のグループで、残る 2つは同型類で繋がるという性質を持っている。（2つのグループは、無限個の族をなし、11個のグループの中に含まれることがあり、9個のグループをなることがある。） (ja) Классификация Бьянки — классификация вещественных трёхмерных алгебр и групп Ли.Названа в честь Луиджи Бьянки, который доказал её в 1898 году. Классификация содержит 11 классов; 9 из них содержат по одной алгебре, а два содержат континуальное семейство алгебр.(Иногда две группы включаются в бесконечные семейства, давая 9 вместо 11 классов.) Термин классификация Бьянки также используется для аналогичных классификаций в других размерностях, а также для классификаций комплексных алгебр Ли. (ru) 数学中，比安基分类（Bianchi classification），以路易吉·比安基命名，将3维实李代数分为11类，其中9个是单独的组，另两类具有连续统同构类。（有两个组有时也包含在无穷族中，从而分为9类。）“比安基分类”也用于其它维数的类似分类。 (zh) In mathematics, the Bianchi classification provides a list of all real 3-dimensional Lie algebras (up to isomorphism). The classification contains 11 classes, 9 of which contain a single Lie algebra and two of which contain a continuum-sized family of Lie algebras. (Sometimes two of the groups are included in the infinite families, giving 9 instead of 11 classes.) The classification is important in geometry and physics, because the associated Lie groups serve as symmetry groups of 3-dimensional Riemannian manifolds. It is named for Luigi Bianchi, who worked it out in 1898. (en)
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Wikipage revision ID	1117919018 (xsd:integer)
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