翻訳と辞書 Words near each other ・ Affine combination ・ Affine connection ・ Affine coordinate system ・ Affine curvature ・ Affine differential geometry ・ Affine focal set ・ Affine gauge theory ・ Affine geometry ・ Affine geometry of curves ・ Affine Grassmannian ・ Affine Grassmannian (manifold) ・ Affine group ・ Affine Hecke algebra ・ Affine hull ・ Affine involution ・ Affine Lie algebra ・ Affine logic ・ Affine manifold ・ Affine manifold (disambiguation) ・ Affine monoid ・ Affine plane ・ Affine plane (incidence geometry) ・ Affine pricing ・ Affine q-Krawtchouk polynomials ・ Affine representation ・ Affine root system ・ Affine shape adaptation ・ Affine space ・ Affine sphere ・ Affine term structure model 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 Affine Lie algebra ： ウィキペディア英語版 Affine Lie algebra In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. It is a Kac–Moody algebra for which the generalized Cartan matrix is positive semi-definite and has corank 1. From purely mathematical point of view, affine Lie algebras are interesting because their representation theory, like representation theory of finite dimensional, semisimple Lie algebras is much better understood than that of general Kac–Moody algebras. As observed by Victor Kac, the character formula for representations of affine Lie algebras implies certain combinatorial identities, the Macdonald identities. Affine Lie algebras play an important role in string theory and conformal field theory due to the way they are constructed: starting from a simple Lie algebra $\backslash mathfrak$, one considers the loop algebra, $L\backslash mathfrak$, formed by the $\backslash mathfrak$-valued functions on a circle (interpreted as the closed string) with pointwise commutator. The affine Lie algebra $\backslash hat$ associated to an automorphism of its Dynkin diagram, the twisted loop algebra $L\_\backslash sigma\backslash mathfrak$ consists of $\backslash mathfrak$-valued functions ''f'' on the real line which satisfy the twisted periodicity condition ''f(x+2π) = σ f(x)''. Their central extensions are precisely the twisted affine Lie algebras. The point of view of string theory helps to understand many deep properties of affine Lie algebras, such as the fact that the characters of their representations transform amongst themselves under the modular group. == Affine Lie algebras from simple Lie algebras == 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「Affine 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.