e/Algebraic group

Information
has gloss	eng: In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. In category theoretic terms, an algebraic group is a group object in the category of algebraic varieties.
lexicalization	eng: Algebraic groups
lexicalization	eng: algebraic group
subclass of	(noun) any number of entities (members) considered as a unit group, grouping
has instance	e/Adelic algebraic group
has instance	e/Algebraic torus
has instance	e/Approximation in algebraic groups
has instance	e/Arithmetic group
has instance	e/BN-pair
has instance	e/Borel subgroup
has instance	e/Bruhat decomposition
has instance	e/Cartan subgroup
has instance	c/Representation theory of algebraic groups
has instance	e/Formal group
has instance	e/Fundamental lemma (automorphic forms)
has instance	e/Geometric invariant theory
has instance	e/Group of Lie type
has instance	e/Group scheme
has instance	e/Hyperspecial subgroup
has instance	e/Jordan–Chevalley decomposition
has instance	e/Kostant polynomial
has instance	e/Langlands decomposition
has instance	e/Lattice (group theory)
has instance	e/Linear algebraic group
has instance	e/Radical of an algebraic group
has instance	e/Restricted Lie algebra
has instance	e/Root datum
has instance	e/Semisimple algebraic group
has instance	e/Severi-Brauer variety
has instance	e/Tannakian category
has instance	e/Unipotent
has instance	e/Witt vector
has instance	e/Étale group scheme

Meaning
German
has gloss	deu: Der mathematische Begriff der algebraischen Gruppe stellt die Synthese aus Gruppentheorie und algebraischer Geometrie dar. Ein zentrales Beispiel ist die Gruppe der invertierbaren n×n-Matrizen.
lexicalization	deu: Algebraische Gruppe
Esperanto
lexicalization	epo: Algebraj grupoj
Finnish
has gloss	fin: Algebrallinen ryhmä määriteltynä k:n yli on varisto G määriteltynä k:n yli, piste e\in G(k) ja morfismit m:G\times G\to G ja i:G\to G jotka toteuttavat ehdot m(e,x)=m(x,e)=x. m(i(x),x)=m(x,i(x))=e. *m(m(x,y),z)=m(x,m(y,z)).
lexicalization	fin: Algebrallinen ryhmä
lexicalization	fin: Algebralliset ryhmät
French
has gloss	fra: En géométrie algébrique, la notion de groupe algébrique est un équivalent des groupes de Lie en géométrie différentielle ou complexe. Un groupe algébrique est une variété algébrique munie d'une loi de groupe compatible avec sa structure de variété algébrique.
lexicalization	fra: Groupe algebrique
lexicalization	fra: Groupe Algébrique
Dutch
has gloss	nld: In de algebraïsche meetkunde is een algebraïsche groep (of groepvariëteit) een groep die een algebraïsche variëteit is, zodanig dat de vermenigvuldiging en de inverse worden gegeven door reguliere functies op de variëteit. In termen, is een algebraïsche groep een groepobject in de categorie van algebraïsche variëteiten.
lexicalization	nld: algebraïsche groep
Russian
lexicalization	rus: Алгебраические группы
Chinese
has gloss	zho: 在代數幾何中，一個代數群（或群簇）是一個群是一個代數簇，其簇之乘與逆由正則函數提供。以范畴论描述，一個代數群是一個於代數簇範疇 (數學)中的群對象。
lexicalization	zho: 代數群

Word:	(case sensitive)
Language:	(ISO 639-3 code, e.g. "eng" for English)

e/Algebraic group

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