翻訳と辞書 Words near each other ・ Formation rule ・ Formation skydiving ・ Formation Z ・ Formations of the Hellenic Army ・ Formations of the Soviet Army ・ Formations of the United States Army ・ Formations of the United States Army (current) ・ Formations of the United States Army during the Mexican Revolution ・ Formations of the United States Army during the Vietnam War ・ Formations of the United States Army during the War on Terrorism ・ Formations of the United States Army during World War I ・ Formations of the United States Army during World War II ・ Formative assessment ・ Formative context ・ Formative epistemology ・ Formal group ・ Formal Invite ・ Formal language ・ Formal learning ・ Formal manifold ・ Formal methods ・ Formal Methods Europe ・ Formal moduli ・ Formal ontology ・ Formal operation ・ Formal organization ・ Formal power series ・ Formal proof ・ Formal Public Identifier ・ Formal scheme 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 Formal group ： ウィキペディア英語版 Formal group In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations. Formal groups are intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology. ==Definitions== A one-dimensional formal group law over a commutative ring ''R'' is a power series ''F''(''x'',''y'') with coefficients in ''R'', such that # ''F''(''x'',''y'') = ''x'' + ''y'' + terms of higher degree # ''F''(''x'', ''F''(''y'',''z'')) = ''F''(''F''(''x'',''y''), ''z'') (associativity). The simplest example is the additive formal group law ''F''(''x'', ''y'') = ''x'' + ''y''. The idea of the definition is that ''F'' should be something like the formal power series expansion of the product of a Lie group, where we choose coordinates so that the identity of the Lie group is the origin. More generally, an ''n''-dimensional formal group law is a collection of ''n'' power series ''F''''i''(''x''1, ''x''2, ..., ''x''''n'', ''y''1, ''y''2, ..., ''y''''n'') in 2''n'' variables, such that # F(x,y) = x + y + terms of higher degree # F(x, F(y,z)) = F(F(x,y), z) where we write F for (''F''1, ..., ''F''''n''), x for (''x''1,..., ''x''''n''), and so on. The formal group law is called commutative if F(x,y) = F(y,x). :Prop. If ''R'' is $\backslash mathbb$-torsion free then any one-dimensional formal group law over ''R'' is commutative. :Proof. The torsion freeness gives us the exponential and logarithm which allows us to write ''F'' as ''F''(''x'',''y'') = exp(log(''x'') + log(''y'')). There is no need for an axiom analogous to the existence of an inverse for groups, as this turns out to follow automatically from the definition of a formal group law. In other words we can always find a (unique) power series G such that F(x,G(x)) = 0. A homomorphism from a formal group law F of dimension ''m'' to a formal group law G of dimension ''n'' is a collection f of ''n'' power series in ''m'' variables, such that ::G(f(x), f(y)) = f(F(x, y)). A homomorphism with an inverse is called an isomorphism, and is called a strict isomorphism if in addition f(x)= x + terms of higher degree. Two formal group laws with an isomorphism between them are essentially the same; they differ only by a "change of coordinates". 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「Formal 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.