結(jié)合代數(shù)表示論基礎(chǔ)（第1卷）

內(nèi)容概要

　《結(jié)合代數(shù)表示論基礎(chǔ)》是一部三卷集的研究生水平的復(fù)合代數(shù)入門(mén)書(shū)籍，是《倫敦?cái)?shù)學(xué)學(xué)會(huì)學(xué)生教程》系列之一。本書(shū)第一卷，主要講述表示論技巧，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，從箭圖和同調(diào)代數(shù)的線性表示角度講述本論題。本書(shū)自成體系，探討該科目的最基本現(xiàn)代應(yīng)用，例如，箭圖理論技巧，覆蓋理論和積分二次型。大量的例子和每章末的練習(xí)使書(shū)中的內(nèi)容更加豐富，容易理解。詳細(xì)的證明是初學(xué)者和自學(xué)者以及想更加詳細(xì)了解復(fù)合代數(shù)表示論知識(shí)的讀者相當(dāng)十分有益。目次：代數(shù)和模型；箭圖和代數(shù)；表示論和模型；auslander-reirten理論；nakayama代數(shù)和表示-有限群代數(shù)；tilting理論；表示有限遺傳代數(shù)；覆蓋代數(shù)；直向模?！?讀者對(duì)象：適用于代數(shù)表示論和數(shù)學(xué)的相關(guān)理論。

作者簡(jiǎn)介

作者：（加拿大）阿瑟姆（Assem.I.）

書(shū)籍目錄

0.introduction i.algebras and modules 1.1.algebras 1.2.modules 1.3.semisimple modules and the radical of a module 1.4.direct sum decompositions 1.5.projective and injective modules 1.6.basic algebras and embeddings of module categories 1.7.exercises ii.quivers and algebras ii.1.quivers and path algebras ii.2.admissible ideals and quotients of the path algebra ii.3.the quiver of a finite dimensional algebra ii.4.exercises iii.representations and modules iii.1.representations of bound quivers iii.2.the simple, projective, and injective modules iii.3.the dimension vector of a module and the euler characteristic iii.4.exercises iv.auslander-reiten theory iv.1.irreducible morphisms and almost split sequences iv.2.the auslander-reiten translations iv.3.the existence of almost split sequences iv.4.the auslander-reiten quiver of an algebra iv.5.the first brauer-thrall conjecture iv.6.functorial approach to almost split sequences iv.7.exercises v.nakayama algebras and representation-finite group algebras v.1.the loewy series and the loewy lehgth of a module v.2.uniserial modules and right serial algebras v.3.nakayama algebras v.4.almost split sequences for nakayama algebras v.5.representation-finite group algebras v.6.exercises vi.tilting theory via.torsion pairs vi.2.partial tilting modules and tilting modules vi.3.the tilting theorem of brenner and butler vi.4.consequences of the tilting theorem vi.5.separating and splitting tilting modules vi.6.torsion pairs induced by tilting modules vi.7.exercises vii.representation-finite hereditary algebras vii.1.hereditary algebras vii.2.the dynkin and euclidean graphs vii.3.integral quadratic forms vii.4.the quadratic form of a quiver vii.5.reflection functors and gabriel's theorem vii.6.exercises viii.tilted algebras viii.1.sections in translation quivers viii.2.representation-infinite hereditary algebras viii.3.tilted algebras viii.4.projectives and injectives in the connecting component viii.5.the criterion of liu and skowrofiski viii.6.exercises ix.directing modules and postprojective components ix.1.directing modules ix.2.sincere directing modules ix.3.representation-directed algebras ix.4.the separation condition ix.5.algebras such that all projectives are postprojective ix.6.gentle algebras and tilted algebras of type an ix.7.exercises a.appendix.categories, functors, and homology a.1.categories a.2.functors a.3.the radical of a category a.4.homological algebra a.5.the group of extensions a.6.exercises bibliography index list of symbols

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