The optimal version of Hua's fundamental theorem of geometry of square matrices - the low dimensional case

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• 作者：Wen-ling Huang^a ; ^b ; ^{huang@math.uni-hamburg.de" class="auth_mail" title="E-mail the corresponding author} ; ^{huang@informatik.uni-bremen.de" class="auth_mail" title="E-mail the corresponding author} ; Peter &Scaron ; emrl^c ; ^{peter.semrl@fmf.uni-lj.si" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A03 ; 51A99
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：498
• 期：Complete
• 页码：21-57
• 全文大小：540 K

文摘

Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379514005473&_mathId=si1.gif&_user=111111111&_pii=S0024379514005473&_rdoc=1&_issn=00243795&md5=457faa46d768e51bbde8a1444098dfaf" title="Click to view the MathML source">Dclass="mathContainer hidden">class="mathCode">$\mathbb{D}$ be any division ring and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379514005473&_mathId=si2.gif&_user=111111111&_pii=S0024379514005473&_rdoc=1&_issn=00243795&md5=f2a512a157ac20eb5289a73a51842aa2" title="Click to view the MathML source">p,qclass="mathContainer hidden">class="mathCode">$p,q$ positive integers. The optimal version of Hua's fundamental theorem of geometry of square matrices has been known in all dimensions but the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379514005473&_mathId=si104.gif&_user=111111111&_pii=S0024379514005473&_rdoc=1&_issn=00243795&md5=32446c1890411a3337983c02f2dbb2bf" title="Click to view the MathML source">2×2class="mathContainer hidden">class="mathCode">$2\times 2$ case. We solve the remaining case by describing the general form of adjacency preserving maps class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379514005473&_mathId=si156.gif&_user=111111111&_pii=S0024379514005473&_rdoc=1&_issn=00243795&md5=2ffe49fc873ec89ced93cb2d9f309a12" title="Click to view the MathML source">ϕ:M₂(D)→M_p×q(D)class="mathContainer hidden">class="mathCode">$\varphi :M_2(\mathbb{D})\to M_{p\times q}(\mathbb{D})$. One of the main tools is a slight modification of known non-surjective versions of the fundamental theorem of affine geometry.