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ID:34670591
大小:312.28 KB
页数:25页
时间:2019-03-09
《7D dissident maps》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、DissidentMapsontheSeven-DimensionalEuclideanSpaceErnstDieterichandLarsLindbergAbstractAdissidentmaponanite-dimensionaleuclideanvectorspaceVisunderstoodtobealinearmap:V^V!Vsuchthatv;w;(v^w)arelinearlyindependentwheneverv;w2Vare.Thisnotionofadissidentmapprovidesalinkbetweenseeminglydivers
2、easpectsofrealgeometricalgebra,therebyrevealingitsshiftingsignicance.Whileitgeneralizesontheonehandtheclassicalnotionofavectorproduct,itspecializesontheotherhandthestructureofarealdivisionalgebra.MoreoverityieldsnaturallyalargeclassofselfbijectionsoftheprojectivespaceP(V)manyofwhicharecol
3、lineations,butsomeofwhich,surprisingly,arenot.Dissidentmapsareknowntoexistinthedimensions0,1,3and7only.Inthedimensions0,1and3theyareclassiedcompletelyandirredundantly,butindimension7theyarestillfarfrombeingfullyunderstood.ThepresentarticlecontributestotheclassicationofdissidentmapsonR7wh
4、ichinturncontributestotheclassicationof8-dimensionalrealdivisionalgebras.WestudytwolargeclassesofdissidentmapsonR7.Therstclassisformedbyallcomposeddissidentmaps,obtainedfromavectorpro-ductonR7bycompositionwithadeniteendomorphism.Thesecondclassisformedbyalldoubleddissidentmaps,obtainedas
5、thepurelyimaginarypartsofthestructuresofthose8-dimensionalrealquadraticdivisionalgebraswhicharisefroma4-dimensionalrealquadraticdi-visionalgebrabydoubling.Foreachofthesetwoclassesweexhibitacompletebutredundantclassication,givenbya49-parameterfa-milyofcomposeddissidentmapsanda9-parameterfa
6、milyofdoubleddissidentmapsrespectively.Theproblemofrestrictingthesetwofa-miliessuchastoobtainacompleteandirredundantclassicationarisesnaturally.Regardingthesubproblemofcharacterizingwhentwocom-poseddissidentmapsbelongingtotheexhaustive49-parameterfamilyareisomorphic,wepresentanecessaryand
7、sucientcriterion.Regar-dingtheanalogoussubproblemfortheexhaustive9-parameterfamilyofdoubleddissidentmaps,wepresentasucientcriterionwhichisconjectured,andpartiallyproved,eventobenecessary.Finallywesolvethesubproblemofdescribingthosedissidentmapswhicharebothco
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