| 翻訳と辞書 |
| Brauer algebra ： ウィキペディア英語版 |
Brauer algebra
In mathematics, a Brauer algebra is an algebra introduced by used in the representation theory of the orthogonal group. It plays the same role that the symmetric group does for the representation theory of the general linear group in Schur–Weyl duality.
==Definition==
The Brauer algebra depends on the choice of a positive integer ''n'' and a number ''d'' (which in practice is often the dimension of the fundamental representation of an orthogonal group ''O''''d''). The Brauer algebra has dimension (2''n'')!/2''n''''n''! = (2''n'' − 1)(2''n'' − 3) ··· 5·3·1 and has a basis consisting of all pairings on a set of 2''n'' elements ''X''1, ..., ''X''''n'', ''Y''1, ..., ''Y''''n'' (that is, all perfect matchings of a complete graph ''K''2''n'': any two of the 2''n'' elements may be matched to each other, regardless of their symbols). The elements ''X''''i'' are usually written in a row, with the elements ''Y''''i'' beneath them. The product of two basis elements ''A'' and ''B'' is obtained by first identifying the endpoints in the bottom row of ''A '' and the top row of ''B '' (Figure ''AB '' in the diagram), then deleting the endpoints in the middle row and joining endpoints in the remaining two rows if they are joined, directly or by a path, in ''AB '' (Figure ''AB=nn '' in the diagram).
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「Brauer 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.
|
|