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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 Structurable algebra ： ウィキペディア英語版 Structurable algebra In abstract algebra, a structurable algebra is a certain kind of unital involutive non-associative algebra over a field. For example, all Jordan algebras are structurable algebras (with the trivial involution), as is any alternative algebra with involution, or any central simple algebra with involution. An ''involution'' here means a linear anti-homomorphism whose square is the identity. Assume ''A'' is a unital non-associative algebra over a field, and $x\; \backslash mapsto\; \backslash bar$ is an involution. If we define $V\_z:=(x\backslash bar)z+(z\backslash bar)x-(z\backslash bar)y$, and $()=xy-yx$, then we say ''A'' is a ''structurable algebra'' if: $(,\; V\_)\; =\; V\_\; -\; V\_.$ Structurable algebras were introduced by Allison in 1978.〔Garibaldi, p.658〕 The Kantor–Koecher–Tits construction produces a Lie algebra from any Jordan algebra, and this construction can be generalized so that a Lie algebra can be produced from an structurable algebra. Moreover, Allison proved over fields of characteristic zero that a structurable algebra is central simple if and only if the corresponding Lie algebra is central simple.〔 Another example of a structurable algebra is a 56-dimensional non-associative algebra originally studied by Brown in 1963, which can be constructed out of an Albert algebra. When the base field is algebraically closed over characteristic not 2 or 3, the automorphism group of such an algebra has identity component equal to the simply connected exceptional algebraic group of type E6.〔Garibaldi, p.660〕 ==References== 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「Structurable 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.