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Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram



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Autore: Bertram Wolfgang <1965-> Visualizza persona
Titolo: Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram Visualizza cluster
Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2008]
©2008
Descrizione fisica: 1 online resource (218 p.)
Disciplina: 510 s
512/.482
Soggetto topico: Infinite dimensional Lie algebras
Infinite-dimensional manifolds
Symmetric spaces
Geometry, Differential
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references (pages 199-202).
Nota di contenuto: ""Contents""; ""Introduction""; ""I. Basic notions""; ""1. Differential calculus""; ""2. Manifolds""; ""3. Tangent bundle and general fiber bundles""; ""4. The Lie bracket of vector fields""; ""5. Lie groups and symmetric spaces: basic facts""; ""II. Interpretation of tangent objects via scalar extensions""; ""6. Scalar extensions. I: Tangent functor and dual numbers""; ""7. Scalar extensions. II: Higher order tangent functors""; ""8. Scalar extensions. Ill: Jet functor and truncated polynomial rings""; ""III. Second order differential geometry""
""9. The structure of the tangent bundle of a vector bundle""""10. Linear connections. I: Linear structures on bilinear bundles""; ""11. Linear connections. II: Sprays""; ""12. Linear connections. Ill: Covariant derivative""; ""13. Natural operations. I: Exterior derivative of a one-form""; ""14. Natural operations. II: The Lie bracket revisited""; ""IV. Third and higher order differential geometry""; ""15. The structure of T[sup(k)]F: Multilinear bundles""; ""16. The structure of T[sup(k)]F: Multilinear connections""; ""17. Construction of multilinear connections""; ""18. Curvature""
""19. Linear structures on jet bundles""""20. Shifts and symmetrization""; ""21. Remarks on differential operators and symbols""; ""22. The exterior derivative""; ""V. Lie Theory""; ""23. The three canonical connections of a Lie group""; ""24. The structure of higher order tangent groups""; ""25. Exponential map and Campbell-Hausdorff formula""; ""26. The canonical connection of a symmetric space""; ""27. The higher order tangent structure of symmetric spaces""; ""VI.Diffeomorphism Groups and the exponential jet""; ""28. Group structure on the space of sections of T[sup(k)]M""
""29. The exponential jet for vector fields""""30. The exponential jet of a symmetric space""; ""31. Remarks on the exponential jet of a general connection""; ""32. From germs to jets and from jets to germs""; ""Appendix L. Limitations""; ""Appendix G. Generalizations""; ""Appendix: Multilinear Geometry""; ""BA. Bilinear algebra""; ""MA. Multilinear algebra""; ""SA. Symmetric and shift invariant multilinear algebra""; ""PG. Polynomial groups""; ""References""
Titolo autorizzato: Differential geometry, Lie groups, and symmetric spaces over general base fields and rings  Visualizza cluster
ISBN: 1-4704-0506-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910788851903321
Lo trovi qui: Univ. Federico II
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Serie: Memoirs of the American Mathematical Society ; ; no. 900.