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结合代数表示论基础（第1卷）

作者: [加] 阿瑟姆著

出版社: 世界图书出版公司

出版时间: 2011-01

版次: 1

ISBN: 9787510029691

定价: 59.00

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 459页

正文语种: 英语

分类: 自然科学

58人买过

Theideaofrepresentingacomplexmathematicalobjectbyasimpleroneisasoldasmathematicsitself.Itisparticularlyusefulinclassificationproblems.Forinstance，asinglelineartransformationonafinitedimen-sionalvectorspaceisveryadequatelycharacterisedbyitsreductiontoitsrationaloritsJordancanonicalform.ItisnowgenerallyacceptedthattherepresentationtheoryofassociativealgebrastracesitsorigintoHamiltonsdescriptionofthecomplexnumbersbypairsofrealnumbers.Duringthe1930s，E.Noethergavetothetheoryitsmodernsettingbyinterpretingrep-resentationsasmodules.Thatallowedthearsenaloftechniquesdevelopedforthestudyofsemisimplealgebrasaswellasthelanguageandmachineryofhomologicalalgebraandcategorytheorytobeappliedtorepresentationtheory.Usingthese，thetheorygrewrapidlyoverthepastthirtyyears. 作者：（加拿大）阿瑟姆（Assem.I.） 0.Introduction
I.Algebrasandmodules
1.1.Algebras
1.2.Modules
1.3.Semisimplemodulesandtheradicalofamodule..
1.4.Directsumdecompositions
1.5.Projectiveandinjectivemodules..
1.6.Basicalgebrasandembeddingsofmodulecategories
1.7.Exercises
II.Quiversandalgebras
II.1.Quiversandpathalgebras
II.2.Admissibleidealsandquotientsofthepathalgebra
II.3.Thequiverofafinitedimensionalalgebra
II.4.Exercises
III.Representationsandmodules
III.1.Representationsofboundquivers
III.2.Thesimple，projective，andinjectivemodules
III.3.ThedimensionvectorofamoduleandtheEulercharacteristic
III.4.Exercises
IV.Auslander-Reitentheory
IV.1.Irreduciblemorphismsandalmostsplitsequences
IV.2.TheAuslander-Reitentranslations
IV.3.Theexistenceofalmostsplitsequences
IV.4.TheAuslander-Reitenquiverofanalgebra
IV.5.ThefirstBrauer-Thrallconjecture
IV.6.Functorialapproachtoalmostsplitsequences
IV：7.Exercises
V.Nakayamaalgebrasandrepresentation-finitegroupalgebras1
V.1.TheLoewyseriesandtheLoewylengthofamodule
V.2.Uniserialmodulesandrightserialalgebras
V.3.Nakayamaalgebras
V.4.AlmostsplitsequencesforNakayamaalgebras
V.5.Representation-finitegroupalgebras
V.6.Exercises
CONTENTS
VI.Tiltingtheory
VIA.Torsionpairs
VI.2.Partialtiltingmodulesandtiltingmodules
VI.3.ThetiltingtheoremofBrennerandButler
VIA.Consequencesofthetiltingtheorem
VI.5.Separatingandsplittingtiltingmodules
VI.6.Torsionpairsinducedbytiltingmodules
VI.7.Exercises
VII.Representation-finitehereditaryalgebras
VII.1.Hereditaryalgebras
VII.2.TheDynkinandEuclideangraphs
VII.3.Integralquadraticforms
VII.4.Thequadraticformofaquiver
VII.5.ReflectionfunctorsandGabrielstheorem
VII.6.Exercises
VIII.Tiltedalgebras
VIII.1.Sectionsintranslationquivers
VIII.2.Representation-infinitehereditaryalgebras
VIII.3.Tiltedalgebras
VIII.4.Projectivesandinjectivesintheconnectingcomponent
VIII.5.ThecriterionofLiuandSkowrofiski
VIII.6.Exercises
IX.Directingmodulesandpostprojectivecomponents
IX.1.Directingmodules
IX.2.Sinceredirectingmodules
IX.3.Representation-directedalgebras
IX.4.Theseparationcondition
IX.5.Algebrassuchthatallprojectivesarepostprojective
IX.6.GentlealgebrasandtiltedalgebrasoftypeAn
IX.7.Exercises
A.Appendix.Categoriesfunctorsandhomology
A.1.Categories
A.2.Functors
A.3.Theradicalofacategory
A.4.Homologicalalgebra
A.5.Thegroupofextensions
A.6.Exercises
Bibliography
Index
Listofsymbols
内容简介:
Theideaofrepresentingacomplexmathematicalobjectbyasimpleroneisasoldasmathematicsitself.Itisparticularlyusefulinclassificationproblems.Forinstance，asinglelineartransformationonafinitedimen-sionalvectorspaceisveryadequatelycharacterisedbyitsreductiontoitsrationaloritsJordancanonicalform.ItisnowgenerallyacceptedthattherepresentationtheoryofassociativealgebrastracesitsorigintoHamiltonsdescriptionofthecomplexnumbersbypairsofrealnumbers.Duringthe1930s，E.Noethergavetothetheoryitsmodernsettingbyinterpretingrep-resentationsasmodules.Thatallowedthearsenaloftechniquesdevelopedforthestudyofsemisimplealgebrasaswellasthelanguageandmachineryofhomologicalalgebraandcategorytheorytobeappliedtorepresentationtheory.Usingthese，thetheorygrewrapidlyoverthepastthirtyyears.
作者简介:
作者：（加拿大）阿瑟姆（Assem.I.）
目录:
0.Introduction
I.Algebrasandmodules
1.1.Algebras
1.2.Modules
1.3.Semisimplemodulesandtheradicalofamodule..
1.4.Directsumdecompositions
1.5.Projectiveandinjectivemodules..
1.6.Basicalgebrasandembeddingsofmodulecategories
1.7.Exercises
II.Quiversandalgebras
II.1.Quiversandpathalgebras
II.2.Admissibleidealsandquotientsofthepathalgebra
II.3.Thequiverofafinitedimensionalalgebra
II.4.Exercises
III.Representationsandmodules
III.1.Representationsofboundquivers
III.2.Thesimple，projective，andinjectivemodules
III.3.ThedimensionvectorofamoduleandtheEulercharacteristic
III.4.Exercises
IV.Auslander-Reitentheory
IV.1.Irreduciblemorphismsandalmostsplitsequences
IV.2.TheAuslander-Reitentranslations
IV.3.Theexistenceofalmostsplitsequences
IV.4.TheAuslander-Reitenquiverofanalgebra
IV.5.ThefirstBrauer-Thrallconjecture
IV.6.Functorialapproachtoalmostsplitsequences
IV：7.Exercises
V.Nakayamaalgebrasandrepresentation-finitegroupalgebras1
V.1.TheLoewyseriesandtheLoewylengthofamodule
V.2.Uniserialmodulesandrightserialalgebras
V.3.Nakayamaalgebras
V.4.AlmostsplitsequencesforNakayamaalgebras
V.5.Representation-finitegroupalgebras
V.6.Exercises
CONTENTS
VI.Tiltingtheory
VIA.Torsionpairs
VI.2.Partialtiltingmodulesandtiltingmodules
VI.3.ThetiltingtheoremofBrennerandButler
VIA.Consequencesofthetiltingtheorem
VI.5.Separatingandsplittingtiltingmodules
VI.6.Torsionpairsinducedbytiltingmodules
VI.7.Exercises
VII.Representation-finitehereditaryalgebras
VII.1.Hereditaryalgebras
VII.2.TheDynkinandEuclideangraphs
VII.3.Integralquadraticforms
VII.4.Thequadraticformofaquiver
VII.5.ReflectionfunctorsandGabrielstheorem
VII.6.Exercises
VIII.Tiltedalgebras
VIII.1.Sectionsintranslationquivers
VIII.2.Representation-infinitehereditaryalgebras
VIII.3.Tiltedalgebras
VIII.4.Projectivesandinjectivesintheconnectingcomponent
VIII.5.ThecriterionofLiuandSkowrofiski
VIII.6.Exercises
IX.Directingmodulesandpostprojectivecomponents
IX.1.Directingmodules
IX.2.Sinceredirectingmodules
IX.3.Representation-directedalgebras
IX.4.Theseparationcondition
IX.5.Algebrassuchthatallprojectivesarepostprojective
IX.6.GentlealgebrasandtiltedalgebrasoftypeAn
IX.7.Exercises
A.Appendix.Categoriesfunctorsandhomology
A.1.Categories
A.2.Functors
A.3.Theradicalofacategory
A.4.Homologicalalgebra
A.5.Thegroupofextensions
A.6.Exercises
Bibliography
Index
Listofsymbols

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结合代数表示论基础（第1卷）

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