錶示論基本教程 在線電子書 圖書標籤: 錶示論 數學 代數 GTM Algebra 抽象代數 我需要 其餘代數7
發表於2024-12-23
錶示論基本教程 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024
通過修改具體的例子得到抽象模型的結構。弗羅貝尼烏斯互反定理:限製和誘導是一對伴隨的函子,類比hom和張量是一對伴隨函子。錶示論的睏難一在於其定義就是雙對象也就是範疇或者是模,而不是過去的單個對象(或者是嚮量空間或者綫性映射);其次,在於不同的代數結構之間的關係和轉換,錶示論和範疇,模自然關聯:群錶示論是非交換環上模的特例,有限群是半單代數的特例,而半單代數通過wedderburn定理可以同構於可除代數(矩陣是其特例),通過修正矩陣代數中的Jordan正則形式可以得到李代數的抽象分解:直和+冪零(可解)代數。諾特發現代數這個簡化的環結構,用群代數的模等價於有限群錶示。群的正規錶示就是把群代數看做自身的左模 不可約錶示 就是群代數模是單的。楊氏錶 是構造對稱群的不可約錶示的顯示基底
評分更適閤初學者
評分讓newleft幫我把這本書帶到美國真是太明智瞭
評分通過修改具體的例子得到抽象模型的結構。弗羅貝尼烏斯互反定理:限製和誘導是一對伴隨的函子,類比hom和張量是一對伴隨函子。錶示論的睏難一在於其定義就是雙對象也就是範疇或者是模,而不是過去的單個對象(或者是嚮量空間或者綫性映射);其次,在於不同的代數結構之間的關係和轉換,錶示論和範疇,模自然關聯:群錶示論是非交換環上模的特例,有限群是半單代數的特例,而半單代數通過wedderburn定理可以同構於可除代數(矩陣是其特例),通過修正矩陣代數中的Jordan正則形式可以得到李代數的抽象分解:直和+冪零(可解)代數。諾特發現代數這個簡化的環結構,用群代數的模等價於有限群錶示。群的正規錶示就是把群代數看做自身的左模 不可約錶示 就是群代數模是單的。楊氏錶 是構造對稱群的不可約錶示的顯示基底
評分讓newleft幫我把這本書帶到美國真是太明智瞭
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.
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錶示論基本教程 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024