翻訳と辞書 Words near each other ・ Loop braid group ・ Loop counter ・ Loop Creek ・ Loop Creek (West Virginia) ・ Loop Current ・ Loop dependence analysis ・ Loop device ・ Loop di Love ・ Loop diuretic ・ Loop electrical excision procedure ・ Loop entropy ・ LOOP Filmworks ・ Loop fission ・ Loop fusion ・ Loop gain ・ Loop group ・ Loop Guru ・ Loop Halt railway station ・ Loop Head ・ Loop heat pipe ・ Loop I Bubble ・ Loop Independent School District ・ Loop integral ・ Loop interchange ・ Loop invariant ・ Loop inversion ・ Loop jump ・ Loop knitting ・ Loop line ・ Loop line (railway) 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 Loop group ： ウィキペディア英語版 Loop group In mathematics, a loop group is a group of loops in a topological group ''G'' with multiplication defined pointwise. ==Definition== In its most general form a loop group is a group of mappings from a manifold to a topological group . More specifically, let , the circle in the complex plane, and let denote the space of continuous maps , i.e. :$LG\; =\; \backslash ,$ equipped with the compact-open topology. An element of is called a ''loop'' in . Pointwise multiplication of such loops gives the structure of a topological group. Parametrize with , :$\backslash gamma:\backslash theta\; \backslash in\; S^1\; \backslash mapsto\; \backslash gamma(\backslash theta)\; \backslash in\; G,$ and define multiplication in by :$(\backslash gamma\_1\; \backslash gamma\_2)(\backslash theta)\; \backslash equiv\; \backslash gamma\_1(\backslash theta)\backslash gamma\_2(\backslash theta).$ Associativity follows from associativity in . The inverse is given by :$\backslash gamma^:\backslash gamma^(\backslash theta)\; \backslash equiv\; \backslash gamma(\backslash theta)^,$ and the identity by :$e:\backslash theta\; \backslash mapsto\; e\; \backslash in\; G.$ The space is called the free loop group on . A loop group is any subgroup of the free loop group . 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「Loop group」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.