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A uniform description of Riemannian symmetric spaces as Grassmannians using magic square. / CUHK electronic theses & dissertations collection

In this thesis we introduce and study the (i) Grassmannian, (ii) Lagrangian Grassmannian, and (iii) double Lagrangian Grassmannian of subspaces in ( A ⊗ B )n, where A and B are normed division algebras, i.e. R,C,H or O . / This gives a simple and uniform description of all symmetric spaces. This is analogous to Tits magic square description for simple Lie algebras. / We show that every irreducible compact Riemannian symmetric space X must be one of these Grassmannian spaces (up to a finite cover) or a compact simple Lie group. Furthermore, its noncompact dual symmetric space is the open sub-manifold of X consisting of spacelike linear subspaces, at least in the classical cases. / Huang, Yongdong. / "July 2007." / Adviser: Naichung Conan Leung. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0353. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 64-65). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343978
Date January 2007
ContributorsHuang, Yongdong., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, theses
Formatelectronic resource, microform, microfiche, 1 online resource (65 p. : ill.)
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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