結(jié)合代數(shù)表示論基礎(chǔ) 第3卷

內(nèi)容概要

　　本書是一部三卷集的研究生水平的復(fù)合代數(shù)入門書籍，是《倫敦數(shù)學(xué)學(xué)會學(xué)生教程》系列之一。本書第三卷，給出了封閉域上有限維復(fù)合代數(shù)表示論的現(xiàn)代技巧，從tame-wild二分法角度講述表示-無限覆蓋代數(shù)。書中包括了歐氏型表示-無限覆蓋代數(shù)的詳細表述，討論了野生型遺傳代數(shù)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(nèi)容更加豐富，容易理解。詳細的證明是初學(xué)者和自學(xué)者以及想更加詳細了解復(fù)合代數(shù)表示論知識的讀者相當十分有益。目次：代數(shù)的管狀延伸和管狀共同延伸；分支代數(shù)；歐氏型覆蓋代數(shù)；野生型遺傳代數(shù)和覆蓋代數(shù)；前景展望?！　∽x者對象：適用于代數(shù)表示論和數(shù)學(xué)的相關(guān)理論。

作者簡介

作者：(波蘭)辛姆森 (Simson.D.)

書籍目錄

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

章節(jié)摘錄

版權(quán)頁：插圖：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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