Classification of involutions of SL(n,k) and SO(2n+1,k)

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dc.contributor.advisor Aloysius Helminck, Committee Chair en_US Wu, Ling en_US 2010-04-02T19:17:01Z 2010-04-02T19:17:01Z 2002-07-17 en_US
dc.identifier.other etd-05202002-085826 en_US
dc.description.abstract In this paper, we classify the involutions of SL(n,k) and SO(2n+1,k), where k is the complex numbers(algebraically closed field in general), real numbers, finite field and p--adic numbers. We did this in a couple of ways: directly and by using the charaterization given in Helminck 2000 paper. In the case of SO(2n+1,k), we restrict the classification of the involutions to theose p-adic fields where -1 is a square. We also identify those isomorphy classes whose fixed point groups are compact and prove the the others are not. The classification in this paper will be the fundamental for the analysis of other cases such SO(2n,k) and SP(n,k). en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject involution en_US
dc.subject symmetric space en_US
dc.subject classification en_US
dc.title Classification of involutions of SL(n,k) and SO(2n+1,k) en_US PhD en_US dissertation en_US Mathematics en_US

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