結合代數表示論基礎 第3卷（簡體書）

《結合代數表示論基礎(英文版第3卷)》是一部三卷集的研究生水平的復合代數入門書籍，是《倫敦數學學會學生教程》系列之一。《結合代數表示論基礎(英文版第3卷)》第三卷，給出了封閉域上有限維復合代數表示論的現代技巧，從tame-wild二分法角度講述表示-無限覆蓋代數。書中包括了歐氏型表示-無限覆蓋代數的詳細表述，討論了野生型遺傳代數上模型范疇的野生行為。大量的例子和每章末的練習使書中的內容更加豐富，容易理解。詳細的證明是初學者和自學者以及想更加詳細了解復合代數表示論知識的讀者相當十分有益。目次：代數的管狀延伸和管狀共同延伸；分支代數；歐氏型覆蓋代數；野生型遺傳代數和覆蓋代數；前景展望。

作者：(波蘭)辛姆森 (Simson.D.)

《結合代數表示論基礎(英文版第3卷)》是由世界圖書出版公司出版的。

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

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.