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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 Special linear Lie algebra ： ウィキペディア英語版 Special linear Lie algebra In mathematics, the special linear Lie algebra of order n (denoted $\backslash mathfrak\_n(F)$) is the Lie algebra of $n\; \backslash times\; n$ matrices with trace zero and with the Lie bracket $():=XY-YX$. This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group. ==Applications== The Lie algebra $\backslash mathfrak\_2(\backslash mathbb)$ is central to the study of special relativity, general relativity and supersymmetry: its fundamental representation is the so-called spinor representation, while its adjoint representation generates the Lorentz group SO(3,1) of special relativity. The algebra $\backslash mathfrak\_2(\backslash mathbb)$ plays an important role in the study of chaos and fractals, as it generates the Möbius group SL(2,R), which describes the automorphisms of the hyperbolic plane, the simplest Riemann surface of negative curvature; by contrast, SL(2,C) describes the automorphisms of the hyperbolic 3-dimensional ball. 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「Special linear 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.