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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 Lie algebra cohomology ： ウィキペディア英語版 Lie algebra cohomology In mathematics, Lie algebra cohomology is a cohomology theory for Lie algebras. It was defined by in order to give an algebraic construction of the cohomology of the underlying topological spaces of compact Lie groups. In the paper above, a specific chain complex, called the Koszul complex, is defined for a module over a Lie algebra, and its cohomology is taken in the normal sense. ==Motivation== If ''G'' is a compact simply connected Lie group, then it is determined by its Lie algebra, so it should be possible to calculate its cohomology from the Lie algebra. This can be done as follows. Its cohomology is the de Rham cohomology of the complex of differential forms on ''G''. This can be replaced by the complex of equivariant differential forms, which can in turn be identified with the exterior algebra of the Lie algebra, with a suitable differential. The construction of this differential on an exterior algebra makes sense for any Lie algebra, so is used to define Lie algebra cohomology for all Lie algebras. More generally one uses a similar construction to define Lie algebra cohomology with coefficients in a module. 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 algebra cohomology」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.