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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Glossary of Lie algebras ： ウィキペディア英語版 Glossary of Lie algebras This is a glossary for the terminology applied in the mathematical theories of Lie algebras. The statements in this glossary mainly focus on the algebraic sides of the concepts, without referring to Lie groups or other related subjects. ==Definition== ; Lie algebra : A vector space $\backslash mathfrak$ over a field $F$ with a binary operation (called the Lie bracket or abbr. bracket) , which satisfies the following conditions: $\backslash forall\; a,b\; \backslash in\; F,\; x,y,z\; \backslash in\; \backslash mathfrak$, :# $()\; =\; a()\; +\; b()$ (bilinearity) :# $()\; =\; 0$ (alternating) :# (Jacobi identity) ; associative algebra : An associative algebra $A$ can be made to a Lie algebra by defining the bracket $()\; =\; xy-yx$ (the commutator of $x,y$) $\backslash forall\; x,y\; \backslash in\; A$ . ; homomorphism : A vector space homomorphism $\backslash phi\; :\; \backslash mathfrak\_1\; \backslash to\; \backslash mathfrak\_2$ is said to be a Lie algebra homomorphism if $\backslash phi(())\; =\; (\backslash phi(x),\; \backslash phi(y))\; \backslash ,\; \backslash forall\; x,y\; \backslash in\; \backslash mathfrak\_1.$ ; adjoint representation : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Glossary of Lie algebras」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.