查看“︁Ado定理”︁的源代码

在[[抽象代數]]中，Ado定理指出每一個有限維的，在一個零[[特徵 (代數)|特徵]]的[[体 (数学)|域]]<math>K</math>上的[[李代數]]<math>L</math>都可被看作是一個用[[交換子]][[李括號]]定義的關於[[方塊矩陣]]的李代數。更為準確地說，定理指出<math>L</math>在<math>K</math>上有一個在有限維[[向量空間]]<math>V</math>上的忠實[[表示论|線性表示]]，使得<math>L</math>與一個<math>V</math>自同态的子代數同構。

雖然對於[[典型群]]的李代數而言，這個結果並不特別，但對於一般情況這則是一個深刻的結果。在應用到一個李群<math>G</math>的實李代數上時，該定理並'''不'''指出<math>G</math>有一個忠實的線性表示（這一般是不正確的），而是指出<math>G</math>總是有一個線性表示與一個[[矩陣群|線性群]]局部同構。定理于1935年由[[喀山联邦大学|喀山国立大学]]的Igor Dmitrievich Ado（{{link-en|Nikolai Chebotaryov|Nikolai Chebotaryov}}的學生）所證明。

定理中對於特徵的限制則與後來由[[岩泽健吉]]和{{link-en|Harish-Chandra|Harish-Chandra}}除去。

==參見==
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* I. D. Ado, ''Note on the representation of finite continuous groups by means of linear substitutions'', Izv. Fiz.-Mat. Obsch. (Kazan'), 7  (1935)  pp.&nbsp;1–43  (Russian language)
*{{Citation | last1=Ado | first1=I. D. | title=The representation of Lie algebras by matrices | url=http://mi.mathnet.ru/eng/umn/v2/i6/p159 | language=ru | mr=0027753 | year=1947 | journal=Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk | issn=0042-1316 | volume=2 | issue=6 | pages=159–173 | accessdate=2012-12-29 | archive-date=2019-09-19 | archive-url=https://web.archive.org/web/20190919024241/http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=6996&option_lang=eng | dead-url=no }} translation in {{Citation | last1=Ado | first1=I. D. | title=The representation of Lie algebras by matrices | mr=0030946 | year=1949 | journal=American Mathematical Society Translations | issn=0065-9290 | volume=1949 | issue=2 | pages=21}}
*{{Citation | last1=Iwasawa | first1=Kenkichi | title=On the representation of Lie algebras | mr=0032613 | year=1948 | journal=Japanese Journal of Mathematics | volume=19 | pages=405–426}}
*{{Citation | last1=Harish-Chandra | title=Faithful representations of Lie algebras | jstor=1969352 | mr=0028829 | year=1949 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=50 | pages=68–76}}
* {{Citation | last1=Hochschild | first1=Gerhard | title=An addition to Ado's theorem | year=1966 | journal=Proc. Amer. Math. Soc. | volume=17 | pages=531–533 | url=http://www.ams.org/journals/proc/1966-017-02/S0002-9939-1966-0194482-0/home.html | accessdate=2012-12-29 | archive-date=2014-05-23 | archive-url=https://web.archive.org/web/20140523225924/http://www.ams.org/journals/proc/1966-017-02/S0002-9939-1966-0194482-0/home.html | dead-url=no }}
* [[Nathan Jacobson]], ''Lie Algebras'', pp.&nbsp;202–203
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[[Category:李代數]]
[[Category:抽象代数定理]]