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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 Homotopy Lie algebra ： ウィキペディア英語版 Homotopy Lie algebra In mathematics, in particular abstract algebra and topology, a homotopy Lie algebra (or $L\_\backslash infty$-algebra) is a generalisation of the concept of a differential graded Lie algebra. To be a little more specific, the Jacobi identity only holds up to homotopy. Therefore, a differential graded Lie algebra can be seen as a homotopy Lie algebra where the Jacobi identity holds on the nose. Homotopy Lie algebras have applications within mathematics and mathematical physics; they are linked, for instance, to the BV formalism much like differential graded Lie algebras are. == Definition == There exists several different definitions of a homotopy Lie algebra, some particularly suited to certain situations more than others. The most traditional definition is via symmetric multi-linear maps, but there also exists a more succinct geometric definition using the language of formal geometry. Here the blanket assumption that the underlying field is of characteristic zero is made. 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「Homotopy 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.