翻訳と辞書 Words near each other ・ Lie a Little Better ・ Lie About Us ・ Lie algebra ・ Lie algebra bundle ・ Lie algebra cohomology ・ Lie algebra extension ・ Lie algebra representation ・ Lie algebra-valued differential form ・ Lie algebroid ・ Lie Back and Enjoy It ・ Lie Back and Think of England ・ Lie bialgebra ・ Lie bialgebroid ・ Lie bracket of vector fields ・ Lie Cliff ・ Lie coalgebra ・ Lie conformal algebra ・ Lie derivative ・ Lie detection ・ Lie Detector (disambiguation) ・ Lie Detector (TV series) ・ Lie Detectors ・ Lie Die ・ Lie Down in Darkness ・ Lie Down in Darkness (Moby song) ・ Lie Down in Darkness (novel) ・ Lie Down in the Light ・ Lie Down with Lions ・ Lie group ・ Lie group action 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 Lie coalgebra ： ウィキペディア英語版 Lie coalgebra In mathematics a Lie coalgebra is the dual structure to a Lie algebra. In finite dimensions, these are dual objects: the dual vector space to a Lie algebra naturally has the structure of a Lie coalgebra, and conversely. ==Definition== Let ''E'' be a vector space over a field ''k'' equipped with a linear mapping $d\backslash colon\; E\; \backslash to\; E\; \backslash wedge\; E$ from ''E'' to the exterior product of ''E'' with itself. It is possible to extend ''d'' uniquely to a graded derivation (this means that, for any ''a'', ''b'' ∈ ''E'' which are homogeneous elements, $d(a\; \backslash wedge\; b)\; =\; (da)\backslash wedge\; b\; +\; (-1)^\; a\; \backslash wedge(db)$) of degree 1 on the exterior algebra of ''E'': :$d\backslash colon\; \backslash bigwedge^\backslash bullet\; E\backslash rightarrow\; \backslash bigwedge^\; E.$ Then the pair (''E'', ''d'') is said to be a Lie coalgebra if ''d''2 = 0, i.e., if the graded components of the exterior algebra with derivation $(\backslash bigwedge^$ * E, d) form a cochain complex: :$E\backslash \; \backslash rightarrow^\backslash \; E\backslash wedge\; E\backslash \; \backslash rightarrow^\backslash \; \backslash bigwedge^3\; E\backslash rightarrow^\backslash \; \backslash dots$ 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「Lie coalgebra」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.