群的表示与群的特征（第2版）
出版时间:
2009-05
版次:
2
ISBN:
9787510004582
定价:
49.00
装帧:
平装
开本:
24开
纸张:
胶版纸
页数:
458页
正文语种:
英语
33人买过
-
Representationtheoryisconcernedwiththewaysofwritingagroupasagroupofmatrices.Notonlyisthetheorybeautifulinitsownright，butitalsoprovidesoneofthekeystoaproperunderstandingoffinitegroups.Forexample，itisoftenvitaltohaveaconcretedescriptionofaparticulargroup；thisisachievedbyfindingarepresentationofthegroupasagroupofmatrices.Moreover，bystudyingthedifferentrepresentationsofthegroup，itispossibletoproveresultswhichlieoutsidetheframeworkofrepresentationtheory.Onesimpleexample：allgroupsoforderp2（wherepisaprimenumber）areabelian；thiscanbeshownquicklyusingonlygrouptheory，butitisalsoaconsequenceofbasicresultsaboutrepresentations. Preface
1Groupsandhomomorphisms
2Vectorspacesandlineartransformations
3Grouprepresentations
4FG-modules
5FG-submodulesandreducibility
6Groupalgebras
7FG-homomorphisms
8Maschke'sTheorem
9Schur'sLemma
10Irreduciblemodulesandthegroupalgebra
11Moreonthegroupalgebra
12Conjugacyclasses
13Characters
14Innerproductsofcharacters
15Thenumberofirreduciblecharacters
16Charactertablesandorthogonalityrelations
17Normalsubgroupsandliftedcharacters
18Someelementarycharactertables
19Tensorproducts
20Restrictiontoasubgroup
21Inducedmodulesandcharacters
22Algebraicintegers
23Realrepresentations
24Summaryofpropertiesofcharactertables
25Charactersofgroupsoforderpq
26Charactersofsomep-groups
27Charactertableofthesimplegroupoforder168
28CharactertableofGL（2，q）
29Permutationsandcharacters
30Applicationstogrouptheory
31Burnside'sTheorem
32Anapplicationofrepresentationtheorytomolecularvibration
Solutionstoexercises
Bibliography
Index
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内容简介:
Representationtheoryisconcernedwiththewaysofwritingagroupasagroupofmatrices.Notonlyisthetheorybeautifulinitsownright，butitalsoprovidesoneofthekeystoaproperunderstandingoffinitegroups.Forexample，itisoftenvitaltohaveaconcretedescriptionofaparticulargroup；thisisachievedbyfindingarepresentationofthegroupasagroupofmatrices.Moreover，bystudyingthedifferentrepresentationsofthegroup，itispossibletoproveresultswhichlieoutsidetheframeworkofrepresentationtheory.Onesimpleexample：allgroupsoforderp2（wherepisaprimenumber）areabelian；thiscanbeshownquicklyusingonlygrouptheory，butitisalsoaconsequenceofbasicresultsaboutrepresentations.
-
目录:
Preface
1Groupsandhomomorphisms
2Vectorspacesandlineartransformations
3Grouprepresentations
4FG-modules
5FG-submodulesandreducibility
6Groupalgebras
7FG-homomorphisms
8Maschke'sTheorem
9Schur'sLemma
10Irreduciblemodulesandthegroupalgebra
11Moreonthegroupalgebra
12Conjugacyclasses
13Characters
14Innerproductsofcharacters
15Thenumberofirreduciblecharacters
16Charactertablesandorthogonalityrelations
17Normalsubgroupsandliftedcharacters
18Someelementarycharactertables
19Tensorproducts
20Restrictiontoasubgroup
21Inducedmodulesandcharacters
22Algebraicintegers
23Realrepresentations
24Summaryofpropertiesofcharactertables
25Charactersofgroupsoforderpq
26Charactersofsomep-groups
27Charactertableofthesimplegroupoforder168
28CharactertableofGL（2，q）
29Permutationsandcharacters
30Applicationstogrouptheory
31Burnside'sTheorem
32Anapplicationofrepresentationtheorytomolecularvibration
Solutionstoexercises
Bibliography
Index
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