翻訳と辞書 Words near each other ・ Lie group action ・ Lie group decomposition ・ Lie groupoid ・ Lie group–Lie algebra correspondence ・ Lie in Our Graves ・ Lie Kim Hok ・ Lie Lie Lie ・ Lie Lie Live ・ Lie Lover Lie ・ Lie of the Land ・ Lie on file ・ Lie point symmetry ・ Lie product formula ・ Lie sphere ・ Lie sphere geometry ・ Lie superalgebra ・ Lie Tek Swie ・ Lie theory ・ Lie to Me ・ Lie to Me (2011 TV series) ・ Lie to Me (album) ・ Lie to Me (Bon Jovi song) ・ Lie to Me (Buffy the Vampire Slayer) ・ Lie to Me (Cole Plante song) ・ Lie to Me (Denial) ・ Lie to Me (disambiguation) ・ Lie to Me (Gary Barlow song) ・ Lie to You for Your Love ・ Lie with Me ・ Lie Yukou Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lie superalgebra ： ウィキペディア英語版 Lie superalgebra In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. In most of these theories, the ''even'' elements of the superalgebra correspond to bosons and ''odd'' elements to fermions (but this is not always true; for example, the BRST supersymmetry is the other way around). ==Definition== Formally, a Lie superalgebra is a (nonassociative) Z2-graded algebra, or ''superalgebra'', over a commutative ring (typically R or C) whose product , called the Lie superbracket or supercommutator, satisfies the two conditions (analogs of the usual Lie algebra axioms, with grading): Super skew-symmetry: :$()=-(-1)^().\backslash$ The super Jacobi identity: :$is\; the\; sum\; of\; degree\; of\; x\; and\; y\; modulo\; 2.$ One also sometimes adds the axioms $()=0$ for |''x''|=0 (if 2 is invertible this follows automatically) and $(),x]=0$ for |''x''|=1 (if 3 is invertible this follows automatically). When the ground ring is the integers or the Lie superalgebra is a free module, these conditions are equivalent to the condition that the Poincaré–Birkhoff–Witt theorem holds (and, in general, they are necessary conditions for the theorem to hold). Just as for Lie algebras, the universal enveloping algebra of the Lie superalgebra can be given a (algebra )] structure. 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「Lie superalgebra」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.