翻訳と辞書 Words near each other ・ ADE (chemotherapy) ・ Ade (drink suffix) ・ Ade (given name) ・ Ade (surname) ・ ADE 651 ・ Ade Adebisi ・ Ade Adepitan ・ Ade Akinbiyi ・ Ade Alleyne-Forte ・ Ade at Sea ・ Ade Azeez ・ Ade Bajomo ・ Ade Bethune ・ Ade Capone ・ Ade Chandra ・ ADE classification ・ Ade Coker ・ Ade Dagunduro ・ Ade Easily ・ Ade Edmondson ・ Ade Fuqua ・ Ade Gardner ・ Ade Hamnett ・ Ade Ipaye ・ Ade Iwan Setiawan ・ Ade Jantra Lukmana ・ Ade Jimoh ・ Ade Kali ・ Ade Kannu ・ Ade Mafe 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 ADE classification ： ウィキペディア英語版 ADE classification In mathematics, the ADE classification (originally ''A-D-E'' classifications) is the complete list of simply laced Dynkin diagrams or other mathematical objects satisfying analogous axioms; "simply laced" means that there are no multiple edges, which corresponds to all simple roots in the root system forming angles of $\backslash pi/2\; =\; 90^\backslash circ$ (no edge between the vertices) or $2\backslash pi/3\; =\; 120^\backslash circ$ (single edge between the vertices). The list comprises :$A\_n,\; \backslash ,\; D\_n,\; \backslash ,\; E\_6,\; \backslash ,\; E\_7,\; \backslash ,\; E\_8.$ These comprise two of the four families of Dynkin diagrams (omitting $B\_n$ and $C\_n$), and three of the five exceptional Dynkin diagrams (omitting $F\_4$ and $G\_2$). This list is non-redundant if one takes $n\; \backslash geq\; 4$ for $D\_n.$ If one extends the families to include redundant terms, one obtains the exceptional isomorphisms :$D\_3\; \backslash cong\; A\_3,\; E\_4\; \backslash cong\; A\_4,\; E\_5\; \backslash cong\; D\_5,$ and corresponding isomorphisms of classified objects. The question of giving a common origin to these classifications, rather than a posteriori verification of a parallelism, was posed in . The ''A'', ''D'', ''E'' nomenclature also yields the simply laced finite Coxeter groups, by the same diagrams: in this case the Dynkin diagrams exactly coincide with the Coxeter diagrams, as there are no multiple edges. == Lie algebras == In terms of complex semisimple Lie algebras: * $A\_n$ corresponds to $\backslash mathfrak\_(\backslash mathbf),$ the special linear Lie algebra of traceless operators, * $D\_n$ corresponds to $\backslash mathfrak\_(\backslash mathbf),$ the even special orthogonal Lie algebra of even-dimensional skew-symmetric operators, and * $E\_6,\; E\_7,\; E\_8$ are three of the five exceptional Lie algebras. In terms of compact Lie algebras and corresponding simply laced Lie groups: * $A\_n$ corresponds to $\backslash mathfrak\_,$ the algebra of the special unitary group $SU(n+1);$ * $D\_n$ corresponds to $\backslash mathfrak\_(\backslash mathbf),$ the algebra of the even projective special orthogonal group $PSO(2n)$, while * $E\_6,\; E\_7,\; E\_8$ are three of five exceptional compact 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「ADE classification」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.