Jordan theoretic G-orbits and flag varieties [Elektronische Ressource] / vorgelegt von Benjamin Schwarz

Benjamin Schwarz

Description

Jordan theoreticG-orbitsand flag varietiesDissertationzur Erlangung des Doktorgradesder Naturwissenschaften (Dr. rer. nat.)demFachbereich Mathematik und Informatikder Philipps-Universität Marburg(Hochschulkennziffer 1180)vorgelegt vonBenjamin Schwarzaus StadeMarburg, im August 2010Prof. Dr. H. UpmeierErstgutachter:Prof. Dr. J. HilgertZweitgutachter:25. August 2010Eingereicht am:21. September 2010Disputation am:ContentsIntroduction iiiPart 1. Methods for Jordan theoretic varieties 1Chapter 1. Jordan algebras 31.1. Basic structure 31.2. Idempotents and Peirce decomposition 41.3. Jordan algebras with unit element 41.4. Euclidean Jordan algebras 5Chapter 2. Jordan triple systems 72.1. Basic structure 72.2. Conjugate Jordan triple systems 92.3. Connection to Jordan algebras 92.4. Tripotents and the spectral theorem 102.5. Pseudo-inverse elements and generalized Peirce decompositions 122.6. Peirce equivalence 182.7. Bergman operators and the quasi-inverse 202.8. Morphisms and the structure group 232.9. Induced Jordan algebra denominators 262.10. Simple triple systems and their classification 28Chapter 3. Analytic structures 313.1. Manifolds and substructures 313.2. Quotient manifolds 333.3. Analytic structures on Jordan triple systems 363.4. Functional calculus 433.5. Bounded symmetric domains 47Part 2. Orbit structures on the symmetric Grassmannian variety 51Chapter 4. Grassmannian variety 534.1. Loos’ construction 534.2.

Sujets

• Mathematics

Informations

• Publié par: philipps-universitat_marburg
• Publié le: 01 janvier 2010
• Nombre de lectures: 25
• Langue: Deutsch
• Poids de l'ouvrage: 1 Mo

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