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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 Pre-Lie algebra ： ウィキペディア英語版 Pre-Lie algebra In mathematics, a pre-Lie algebra is an algebraic structure on a vector space, that describes some properties of objects such as rooted trees and vector fields on affine space. The notion of pre-Lie algebra has been introduced by Murray Gerstenhaber in his work on deformations of algebras. Pre-Lie algebras have been considered under some other names, among which one can cite left-symmetric algebras, right-symmetric algebras or Vinberg algebras. == Definition == A pre-Lie algebra $(V,\backslash triangleleft)$ is a vector space $V$ with a bilinear map $\backslash triangleleft\; :\; V\; \backslash otimes\; V\; \backslash to\; V$, satisfying the relation $$ (x \triangleleft y) \triangleleft z - x \triangleleft (y \triangleleft z) = (x \triangleleft z) \triangleleft y - x \triangleleft (z \triangleleft y). This identity can be seen as the invariance of the associator $(x,y,z)\; =\; (x\; \backslash triangleleft\; y)\; \backslash triangleleft\; z\; -\; x\; \backslash triangleleft\; (y\; \backslash triangleleft\; z)$ under the exchange of the two variables $y$ and $z$. Every associative algebra is hence also a pre-Lie algebra, as the associator vanishes identically. 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「Pre-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.