Cartan subalgebra
In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra of a Lie algebra that is self-normalising (if for all , then ). They were introduced by Élie Cartan in his doctoral thesis. It controls the representation theory of a semi-simple Lie algebra over a field of characteristic . Kac–Moody algebras and generalized Kac–Moody algebras also have subalgebras that play the same role as the Cartan subalgebras of semisimple Lie algebras (over a field of characteristic zero).
Cartan subalgebraAffine actionAlgebraic characterAlgebraic torusBorel subalgebraBorel subgroupCSACartan algebraCartan matrixCarter subgroupCategory OChevalley restriction theoremChevalley theoremClebsch–Gordan coefficients for SU(3)Complex Lie algebraConformal field theoryDemazure moduleDirectional derivativeDynkin diagramE6 (mathematics)E7 (mathematics)E8 (mathematics)Engel subalgebraGell-Mann matricesGeneralizations of Pauli matricesGeneralized Kac–Moody algebraGlossary of Lie groups and Lie algebrasHarish-Chandra isomorphismInfinitesimal characterKac–Moody algebraKostant's convexity theoremList of things named after Élie CartanLittelmann path modelMaximal torusMonster Lie algebraNilpotent Lie algebraNonlinear realizationOrbit methodPainlevé transcendentsRank (Lie algebra)
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Cartan subalgebra
In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra of a Lie algebra that is self-normalising (if for all , then ). They were introduced by Élie Cartan in his doctoral thesis. It controls the representation theory of a semi-simple Lie algebra over a field of characteristic . Kac–Moody algebras and generalized Kac–Moody algebras also have subalgebras that play the same role as the Cartan subalgebras of semisimple Lie algebras (over a field of characteristic zero).
has abstract
In der Mathematik, speziell in ...... Algebra der Diagonalmatrizen.
@de
In mathematics, a Cartan subal ...... field of characteristic zero).
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В математиці, зокрема теорії а ...... зького математика Елі Картана.
@uk
Подалгебра Картана — нильпотен ...... ённое представление группы Ли.
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在数学中，嘉当子代数（Cartan subalgebra，缩写为 CSA），是一个李代数 的自正规化（如果 对所有 ，那么）、幂零子代数，通常用 表示。
@zh
数学において，カルタン部分環（カルタンぶぶんかん，英: Ca ...... ある．エリ・カルタンによって彼の博士論文において導入された．
@ja
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label
Cartan subalgebra
@en
Cartan-Unteralgebra
@de
Подалгебра Картана
@ru
Підалгебра Картана
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カルタン部分環
@ja
嘉当子代数
@zh
카르탕 부분 대수
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authorlink
Vladimir L. Popov
@en
first
V.L.
@en
last
Popov
@en
title
Cartan subalgebra
@en
wikiPageUsesTemplate
subject
type
comment
In der Mathematik, speziell in ...... Algebra der Diagonalmatrizen.
@de
In mathematics, a Cartan subal ...... field of characteristic zero).
@en
В математиці, зокрема теорії а ...... зького математика Елі Картана.
@uk
Подалгебра Картана — нильпотен ...... ённое представление группы Ли.
@ru
在数学中，嘉当子代数（Cartan subalgebra，缩写为 CSA），是一个李代数 的自正规化（如果 对所有 ，那么）、幂零子代数，通常用 表示。
@zh
数学において，カルタン部分環（カルタンぶぶんかん，英: Ca ...... ある．エリ・カルタンによって彼の博士論文において導入された．
@ja