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Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
| Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram |
| Autore | Bertram Wolfgang <1965-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2008] |
| Descrizione fisica | 1 online resource (218 p.) |
| Disciplina |
510 s
512/.482 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Infinite dimensional Lie algebras
Infinite-dimensional manifolds Symmetric spaces Geometry, Differential |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0506-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910480857603321 |
Bertram Wolfgang <1965->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2008] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
| Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram |
| Autore | Bertram Wolfgang <1965-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2008] |
| Descrizione fisica | 1 online resource (218 p.) |
| Disciplina |
510 s
512/.482 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Infinite dimensional Lie algebras
Infinite-dimensional manifolds Symmetric spaces Geometry, Differential |
| ISBN | 1-4704-0506-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910788851903321 |
|
Bertram Wolfgang <1965->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2008] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram
| Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / / Wolfgang Bertram |
| Autore | Bertram Wolfgang <1965-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2008] |
| Descrizione fisica | 1 online resource (218 p.) |
| Disciplina |
510 s
512/.482 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Infinite dimensional Lie algebras
Infinite-dimensional manifolds Symmetric spaces Geometry, Differential |
| ISBN | 1-4704-0506-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910819101003321 |
|
Bertram Wolfgang <1965->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2008] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||