翻訳と辞書 Words near each other ・ Poisson ring ・ Poisson sampling ・ Poisson scatter theorem ・ Poisson summation formula ・ Poisson superalgebra ・ Poisson supermanifold ・ Poisson Volant ・ Poisson wavelet ・ Poisson's equation ・ Poisson's ratio ・ Poisson, Saône-et-Loire ・ Poissonia ・ Poissonnière (Paris Métro) ・ Poissons ・ Poisson–Boltzmann equation ・ Poisson–Lie group ・ Poissy ・ Poisvilliers ・ Poisy ・ Poitea ・ Poitea carinalis ・ Poitevin ・ Poitevin (dog) ・ Poitevin dialect ・ Poitevin horse ・ Poitevin-Saintongeais ・ Poitier ・ Poitier Meets Plato ・ Poitiers ・ Poitiers Basket 86 Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Poisson–Lie group ： ウィキペディア英語版 Poisson–Lie group In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra structure on the manifold. The algebra of a Poisson–Lie group is a Lie bialgebra. ==Definition== A Poisson–Lie group is a Lie group ''G'' equipped with a Poisson bracket for which the group multiplication $\backslash mu:G\backslash times\; G\backslash to\; G$ with $\backslash mu(g\_1,\; g\_2)=g\_1g\_2$ is a Poisson map, where the manifold ''G''×''G'' has been given the structure of a product Poisson manifold. Explicitly, the following identity must hold for a Poisson–Lie group: :$\backslash \; (gg\text{'})\; =$ \ (g') + \\} (g) where ''f''1 and ''f''2 are real-valued, smooth functions on the Lie group, while ''g'' and ''g are elements of the Lie group. Here, ''Lg'' denotes left-multiplication and ''Rg'' denotes right-multiplication. If $\backslash mathcal$ denotes the corresponding Poisson bivector on ''G'', the condition above can be equivalently stated as :$\backslash mathcal(gg\text{'})\; =\; L\_(\backslash mathcal(g\text{'}))\; +\; R\_(\backslash mathcal(g))$ Note that for Poisson-Lie group always $\backslash (e)\; =\; 0$, or equivalently $\backslash mathcal(e)\; =\; 0$. This means that non-trivial Poisson-Lie structure is never symplectic, not even of constant rank. 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「Poisson–Lie group」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.