Projective embeddings of dual polar spaces arising from a class of alternative division rings |
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| Institution: | 1. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China;2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John''s, Newfoundland A1C 5S7, Canada;3. School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;1. Department of Informatics, University of Bergen, Norway;2. DISIM, University of l''Aquila, Italy;3. Department of Mathematics, University of Trento, Italy;1. College of Chemistry and Materials Science, Fujian Normal University, Fuzhou 350007, China;2. Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, China;3. Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang 621900, China |
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| Abstract: | We discuss some recent results of us regarding a class of polar spaces which includes the nonembeddable polar spaces introduced by Tits Tits, J., “Buildings of spherical type and finite BN-pairs,” Lecture Notes in Mathematics 386, Springer-Verlag, Berlin-New York, 1974]. These results include an elementary construction of the polar space, a construction of a polarized embedding of the corresponding dual polar space and the determination whether this projective embedding is universal and unique (as a polarized embedding). |
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| Keywords: | nonembeddable polar space Cayley-Dickson division algebra alternative division ring dual polar space projective embedding"} {"#name":"keyword" "$":{"id":"kw0060"} "$$":[{"#name":"text" "_":"polarized universal |
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