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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 Toral Lie algebra ： ウィキペディア英語版 Toral Lie algebra In mathematics, a toral Lie algebra is a Lie subalgebra of a general linear Lie algebra all of whose elements are semisimple (or diagonalizable over an algebraically closed field). Equivalently, a Lie algebra is toral if it contains no nonzero nilpotent elements. Over an algebraically closed field, every toral Lie algebra is abelian; thus, its elements are simultaneously diagonalizable. == Semisimple and reductive Lie algebras == A subalgebra ''H'' of a semisimple Lie algebra ''L'' is called toral if the adjoint representation of ''H'' on ''L'', ''ad''(''H'')⊂''gl''(''L'') is a toral Lie algebra. A maximal toral Lie subalgebra of a finite-dimensional semisimple Lie algebra, or more generally of a finite-dimensional reductive Lie algebra, over an algebraically closed field of characteristic 0 is a Cartan subalgebra and vice versa. In particular, a maximal toral Lie subalgebra in this setting is self-normalizing, coincides with its centralizer, and the Killing form of ''L'' restricted to ''H'' is nondegenerate. For more general Lie algebras, a Cartan algebra may differ from a maximal toral 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「Toral 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.