翻訳と辞書 Words near each other ・ Character mask ・ Character Of Generation ・ Character of Robert E. Howard ・ Character of the Happy Warrior ・ Character orientation ・ Character piece ・ Character race ・ Character sheet ・ Character sketch ・ Character Strengths and Virtues ・ Character structure ・ Character Studio ・ Character sum ・ Character table ・ Character Technical Director ・ Character theory ・ Character theory (media) ・ Character variety ・ Character-count integrity ・ Character-oriented terminal ・ Characterisation (law) ・ Characterisation of pore space in soil ・ Characteristic ・ Characteristic (algebra) ・ Characteristic 2 type ・ Characteristic admittance ・ Characteristic based product configurator ・ Characteristic class ・ Characteristic curve ・ Characteristic energy 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 Character theory ： ウィキペディア英語版 Character theory :''This article refers to the use of the term character theory in mathematics. For the media studies definition, see Character theory (Media).'' For related senses of the word character, see Character (mathematics). In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on the characters, and without any explicit matrix realization of representations themselves. This is possible because a complex representation of a finite group is determined (up to isomorphism) by its character. The situation with representations over a field of positive characteristic, so-called "modular representations", is more delicate, but Richard Brauer developed a powerful theory of characters in this case as well. Many deep theorems on the structure of finite groups use characters of modular representations. == Applications == Characters of irreducible representations encode many important properties of a group and can thus be used to study its structure. Character theory is an essential tool in the classification of finite simple groups. Close to half of the proof of the Feit–Thompson theorem involves intricate calculations with character values. Easier, but still essential, results that use character theory include the Burnside theorem (a purely group-theoretic proof of the Burnside theorem has since been found, but that proof came over half a century after Burnside's original proof), and a theorem of Richard Brauer and Michio Suzuki stating that a finite simple group cannot have a generalized quaternion group as its . 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「Character theory」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.