结合代数表示论基础 第3卷

出版时间：2011-1  出版社：世界图书出版公司  作者：辛姆森  页数：456  

内容概要

　　本书是一部三卷集的研究生水平的复合代数入门书籍，是《伦敦数学学会学生教程》系列之一。本书第三卷，给出了封闭域上有限维复合代数表示论的现代技巧，从tame-wild二分法角度讲述表示-无限覆盖代数。书中包括了欧氏型表示-无限覆盖代数的详细表述，讨论了野生型遗传代数上模型范畴的野生行为。大量的例子和每章末的练习使书中的内容更加丰富，容易理解。详细的证明是初学者和自学者以及想更加详细了解复合代数表示论知识的读者相当十分有益。目次：代数的管状延伸和管状共同延伸；分支代数；欧氏型覆盖代数；野生型遗传代数和覆盖代数；前景展望。　　读者对象：适用于代数表示论和数学的相关理论。

作者简介

作者：(波兰)辛姆森 (Simson.D.)

书籍目录

introduction xv.tubular extensions and tubular coextensions of algebras 　xv.1.one-point extensions and one-point coextensions of algebras 　xv.2.tubular extensions and tubular coextensions of algebras 　xv.3.branch extensions and branch coextensions of algebras 　xv.4.tubular extensions and tubular coextensions of concealed algebras of euclidean type 　xv.5.exercises xvi.branch algebras 　xvi.1.branches and finite line extensions 　xvi.2.tilted algebras of an equioriented type am　xvi.3.exercises xvii. tilted algebras of euclidean type 　xvii.1.stone cones in hereditary standard stable tubes 　xvii.2.tilting with hereditary standard stable tubes 　xvii.3.representation-infinite tilted algebras of euclidean type 　xvii.4.domestic tubular extensions and domestic tubular coextensions of concealed algebras of euclidean type 　xvii.5.a classification of tilted algebras of euclidean type 　xvii.6.a controlled property of the euler form of tilted algebras of euclidean type 　xvii.7.exercises xviii.wild hereditary algebras and tilted algebras of wild type 　xviii.1.regular components 　xviii.2.homomorphisms between regular modules 　xviii.3.perpendicular categories 　xviii.4.wild behaviour of the module category 　xviii.5.tilted algebras of wild type 　xviii.6.exercises xix.tame and wild representation type of algebras 　xix.1.wild representation type 　xix.2.indecomposable modules over the polynomial algebra k[t] 　xix.3.tame representation type 　xix.4.exercises xx.perspectives 　xx.1.components of the auslander-reiten quiver of an algebra 　xx.2.the tits quadratic form of an algebra 　xx.3.tilted and quasitilted algebras 　xx.4.algebras of small homological dimensions 　xx.5.selfinjective algebras of tilted and quasitilted type 　xx.6.related topics and research directions bibliography index list of symbols

章节摘录

版权页：插图：In Volume 3.we study the repsentation-infinite tilted algebras B：End TXo of a Euclidean type Q，where TKQ is a tilting TKQ-module.Wegive a fairlv complete description of their indecomposable modules，theirmodule categories mod B.and the Auslander-Reiten quivers r（mod B）.The aim of the present chapter iS to introduce concepts playing a fun-damental r61e in the classification of arbitrary representation-infinite tiltedalgebras of Euclidean type，presented in Chapter XVII.  In Section 1，we introduce the concepts of a one-point extension and aone-point coextension of an algebra，and we discuss a behavior of almost split sequences under the one-point extension and the one-point coextenS00nprocedure.In Section 2.we introduce the concepts of a tubular extension and atubular coextension of an algebra，and the related concepts of ray tubes and coray tubes.As we shall see in Chapter XVII，the components of a representation-infinite tilted algebra of Euclidean type that are neither postprojective nor preinjective，are ray tubes or coray tubes·In Section 3，we show that the concepts of the tubular extension and thetubular coextension of an algebra coincide with the concepts of a branch extension and a branch coextension of an algebra.  In Section 4，we discuss the structure of the module categories mod／J and mod B'of a tubular extension B and a tubular coextension B'of a concemed algebra A of Euclidean type，and we introduce the concept of thetubular type of such algebras.The study we start in Section 4 is continuedin Chapter XVII.we show there that every representation-infinite tilted al-gebra of Euclidean type is either a domestic tubular extension or a domestictubular coextension of a concealed algebra of Euclidean type.

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《结合代数表示论基础(英文版第3卷)》是由世界图书出版公司出版的。

用户评论 (总计3条)

•   无论是理论还是例子，都非常详细！值得一读。
•   商品没有问题
•   此书很适合初学者，很易读，包装也很好，印刷也很好，排版也很好。
  这本代数表示论内容非常好，我向大家推介这本书。