翻訳と辞書 Words near each other ・ Quasi-constitutionality ・ Quasi-continuous function ・ Quasi-contract ・ Quasi-criminal ・ Quasi-crystals (supramolecular) ・ Quasi-delict ・ Quasi-derivative ・ Quasi-elemental ・ Quasi-empirical method ・ Quasi-empiricism in mathematics ・ Quasi-experiment ・ Quasi-fibration ・ Quasi-finite field ・ Quasi-finite morphism ・ Quasi-foreign corporation ・ Quasi-Frobenius Lie algebra ・ Quasi-Frobenius ring ・ Quasi-Fuchsian group ・ Quasi-geostrophic equations ・ Quasi-harmonic approximation ・ Quasi-Hilda comet ・ Quasi-homogeneous polynomial ・ Quasi-Hopf algebra ・ Quasi-identifier ・ Quasi-invariant measure ・ Quasi-irreversible inhibitor ・ Quasi-isometry ・ Quasi-isomorphism ・ Quasi-judicial body ・ Quasi-judicial proceedings 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 Quasi-Frobenius Lie algebra ： ウィキペディア英語版 Quasi-Frobenius Lie algebra In mathematics, a quasi-Frobenius Lie algebra :$(\backslash mathfrak,(),\backslash beta\; )$ over a field $k$ is a Lie algebra :$(\backslash mathfrak,()\; )$ equipped with a nondegenerate skew-symmetric bilinear form :$\backslash beta\; :\; \backslash mathfrak\backslash times\backslash mathfrak\backslash to\; k$, which is a Lie algebra 2-cocycle of $\backslash mathfrak$ with values in $k$. In other words, ::$\backslash beta\; \backslash left(\backslash left(),Z\backslash right)+\backslash beta\; \backslash left(\backslash left(),Y\backslash right)+\backslash beta\; \backslash left(\backslash left(),X\backslash right)=0$ for all $X$, $Y$, $Z$ in $\backslash mathfrak$. If $\backslash beta$ is a coboundary, which means that there exists a linear form $f\; :\; \backslash mathfrak\backslash to\; k$ such that :$\backslash beta(X,Y)=f(\backslash left()),$ then :$(\backslash mathfrak,(),\backslash beta\; )$ is called a Frobenius Lie algebra. == Equivalence with pre-Lie algebras with nondegenerate invariant skew-symmetric bilinear form == If $(\backslash mathfrak,(),\backslash beta\; )$ is a quasi-Frobenius Lie algebra, one can define on $\backslash mathfrak$ another bilinear product $\backslash triangleleft$ by the formula ::$\backslash beta\; \backslash left(\backslash left(),Z\backslash right)=\backslash beta\; \backslash left(Z\; \backslash triangleleft\; Y,X\; \backslash right)$. Then one has $\backslash left()=X\; \backslash triangleleft\; Y-Y\; \backslash triangleleft\; X$ and :$(\backslash mathfrak,\; \backslash triangleleft)$ is a pre-Lie algebra. 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「Quasi-Frobenius Lie algebra」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.