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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 Temperley–Lieb algebra ： ウィキペディア英語版 Temperley–Lieb algebra In statistical mechanics, the Temperley–Lieb algebra is an algebra from which are built certain transfer matrices, invented by Neville Temperley and Elliott Lieb. It is also related to integrable models, knot theory and the braid group, quantum groups and subfactors of von Neumann algebras. ==Definition== Let $R$ be a commutative ring and fix $\backslash delta\; \backslash in\; R$. The Temperley–Lieb algebra $TL\_n(\backslash delta)$ is the $R$-algebra generated by the elements $U\_1,\; U\_2,\; \backslash ldots,\; U\_$, subject to the Jones relations: *$U\_i^2\; =\; \backslash delta\; U\_i$ for all $1\; \backslash leq\; i\; \backslash leq\; n-1$ *$U\_i\; U\_\; U\_i\; =\; U\_i$ for all $1\; \backslash leq\; i\; \backslash leq\; n-2$ *$U\_i\; U\_\; U\_i\; =\; U\_i$ for all $2\; \backslash leq\; i\; \backslash leq\; n-1$ *$U\_i\; U\_j\; =\; U\_j\; U\_i$ for all $1\; \backslash leq\; i,j\; \backslash leq\; n-1$ such that $|i-j|\; \backslash neq\; 1$ $TL\_n(\backslash delta)$ may be represented diagrammatically as the vector space over noncrossing pairings on a rectangle with ''n'' points on two opposite sides. The five basis elements of $TL\_3(\backslash delta)$ are the following: . Multiplication on basis elements can be performed by placing two rectangles side by side, and replacing any closed loops by a factor of ''δ'', for example: 50px × 50px = 50px50px = δ 50px. The identity element is the diagram in which each point is connected to the one directly across the rectangle from it, and the generator $U\_i$ is the diagram in which the ''i''th point is connected to the ''i+1''th point, the ''2n − i + 1''th point is connected to the ''2n − i''th point, and all other points are connected to the point directly across the rectangle. The generators of $TL\_5(\backslash delta)$ are: From left to right, the unit 1 and the generators U1, U2, U3, U4. The Jones relations can be seen graphically: 50px 50px = δ 50px 50px 50px 50px = 50px 50px 50px = 50px 50px 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「Temperley–Lieb 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.