群与格引论：有限群与正定有理格（国内英文版）

图书标准信息

• 作者 [美]格里斯（Robert L.Griess） 著
• 出版社 高等教育出版社
• 出版时间 2010-05
• 版次 1
• ISBN 9787040292053
• 定价 58.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 251页
• 字数 370千字
• 正文语种 英语

【内容简介】

《群与格引论：有限群与正定有理格（国内英文版）》内容简介：ThelaunchofthisAdvancedLecturesinMathematicsseriesisaimedatkeeping　mathematiciansinformedofthelatestdevelopmentsinmathematics,aswellas　toaidinthelearningofnewmathematicaltopicsbystudentsallovertheworld.
Eachvolumeconsistsofeitheranexpositorymonographoracollectionofsignifi-　cantintroductionstoimportanttopics.Thisseriesemphasizesthehistoryand　sourcesofmotivationforthetopicsunderdiscussion,andalsogivesanoverview　ofthecurrentstatusofresearchineachparticularfield.Thesevolumesarethe　firstsourcetowhichpeoplewillturninordertolearnnewsubjectsandtodis-coverthelatestresultsofmanycutting-edgefieldsinmathematics.

【目录】

1　Introduction
1.1Outlineofthebook
1.2Suggestionsforfurtherreading
1.3Notations,background,conventions
2BilinearForms,QuadraticFormsandTheirIsometryGroups.
2.1Standardresultsonquadraticformsandreflections
2.1.1Principalidealdomains(PIDs)
2.2Linearalgebra
2.2.1Interpretationofnonsingularity
2.2.2Extensionofscalars
2.2.3Cyclicityofthevaluesofarationalbilinea.rform
2.2.4Grammatrix
2.3Discriminantgroup
2.4Relationsbetweenalatticeandsublattices
2.5Involutionsonquadraticspaces
2.6Standardresultsonquadraticformsandreflections,II
2.6.1Involutionsonlattices
2.7Scaledisometries:normdoublersandtriplers
3GeneralResultsonFiniteGroupsandInvariantLattices
3.1Discretenessofrationallattices
3.2Finitenessoftheisometrygroup
3.3ConstructionofaG-invariantbilinearform
3.4Semidirectproductsandwreathproducts
3.5Orthogonaldecompositionoflattices
4RootLatticesofTypesA,D,E
4.1BackgroundfromLietheory
4.2Rootlattices,theirdualsandtheirisometrygroups
4.2.1DefinitionoftheANlattices
……