Universal enveloping algebra
In mathematics, a universal enveloping algebra is the most general (unital, associative) algebra that contains all representations of a Lie algebra. Universal enveloping algebras are used in the representation theory of Lie groups and Lie algebras. For example, Verma modules can be constructed as quotients of the universal enveloping algebra. In addition, the enveloping algebra gives a precise definition for the Casimir operators. Because Casimir operators commute with all elements of a Lie algebra, they can be used to classify representations. The precise definition also allows the importation of Casimir operators into other areas of mathematics, specifically, those that have a differential algebra. They also play a central role in some recent developments in mathematics. In particular, t
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Universal enveloping algebra
In mathematics, a universal enveloping algebra is the most general (unital, associative) algebra that contains all representations of a Lie algebra. Universal enveloping algebras are used in the representation theory of Lie groups and Lie algebras. For example, Verma modules can be constructed as quotients of the universal enveloping algebra. In addition, the enveloping algebra gives a precise definition for the Casimir operators. Because Casimir operators commute with all elements of a Lie algebra, they can be used to classify representations. The precise definition also allows the importation of Casimir operators into other areas of mathematics, specifically, those that have a differential algebra. They also play a central role in some recent developments in mathematics. In particular, t
has abstract
Die universelle einhüllende Al ...... ssoziativen Algebra herkommen.
@de
Em matemática, para qualquer á ...... álgebras adjuntas à esquerda.
@pt
En mathématiques, on peut cons ...... la plupart des propriétés de .
@fr
För varje Liealgebra kan man k ...... ratorer av godtycklig ordning.
@sv
In mathematics, a universal en ...... ential operators on the group.
@en
Универсальная обёртывающая алг ...... для изучения исходной алгебры.
@ru
在數學中，我們可以構造任意李代數 的泛包絡代數 。李代數一般 ...... 理論。在幾何上，泛包絡代數可以解釋為李群上的左不變微分算子。
@zh
리 대수 이론에서, 보편 포락 대수(普遍包絡代數, 영어 ...... 을 만족시키는 곱셈에 대한 교환자로 나타내는 대수이다.
@ko
（普遍）包絡代数（ふへんほうらくだいすう、英: univer ...... 質を満たす単位的結合代数 と準同型写像 の組 のことをいう。
@ja
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id
universal+enveloping+algebra
@en
title
Universal enveloping algebra
@en
wikiPageUsesTemplate
comment
Die universelle einhüllende Al ...... ssoziativen Algebra herkommen.
@de
Em matemática, para qualquer á ...... se esta álgebra de Lie por AL.
@pt
En mathématiques, on peut cons ...... la plupart des propriétés de .
@fr
För varje Liealgebra kan man k ...... ratorer av godtycklig ordning.
@sv
In mathematics, a universal en ...... mathematics. In particular, t
@en
Универсальная обёртывающая алг ...... для изучения исходной алгебры.
@ru
在數學中，我們可以構造任意李代數 的泛包絡代數 。李代數一般 ...... 理論。在幾何上，泛包絡代數可以解釋為李群上的左不變微分算子。
@zh
리 대수 이론에서, 보편 포락 대수(普遍包絡代數, 영어 ...... 을 만족시키는 곱셈에 대한 교환자로 나타내는 대수이다.
@ko
（普遍）包絡代数（ふへんほうらくだいすう、英: univer ...... 質を満たす単位的結合代数 と準同型写像 の組 のことをいう。
@ja
label
Algèbre enveloppante
@fr
Universal enveloping algebra
@en
Universala envelopa alĝebro
@eo
Universell envelopperande algebra
@sv
Universelle einhüllende Algebra
@de
Álgebra envelopante
@pt
Универсальная обёртывающая алгебра
@ru
Універсальна обгортуюча алгебра
@uk
普遍包絡代数
@ja
泛包絡代數
@zh