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Bombay lectures on highest weight representations of infinite dimensional lie algebras
| Bombay lectures on highest weight representations of infinite dimensional lie algebras |
| Autore | Kac Victor G. <1943-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, 2013 |
| Descrizione fisica | 1 online resource (xii, 237 pages) |
| Disciplina | 520 |
| Collana |
Advanced series in mathematical physics
Gale eBooks |
| Soggetto topico |
Infinite dimensional Lie algebras
Quantum field theory |
| ISBN | 981-4522-20-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Preface to the second edition; CONTENTS; Lecture 1; 1.1. The Lie algebra d of complex vector fields on the circle; 1.2. Representations Vα,β of; 1.3. Central extensions of : the Virasoro algebra; Lecture 2; 2.1. Definition of positive-energy representations of Vir; 2.2. Oscillator algebra A; 2.3. Oscillator representations of Vir; Lecture 3; 3.1. Complete reducibility of the oscillator representations of Vir; 3.2. Highest weight representations of Vir; 3.3. Verma representations M(c, h) and irreducible highest weight representations V (c, h) of Vir
11.3. A character identity Lecture 12; 12.1. Preliminaries on sl2; 12.2. A tensor product decomposition of some representations of sl2; 12.3. Construction and unitarity of the discrete series representations of Vir; 12.4. Completion of the proof of the Kac determinant formula; 12.5. On non-unitarity in the region 0 c < 1, h 0; Lecture 13; 13.1. Formal distributions; 13.2. Local pairs of formal distributions; 13.3. Formal Fourier transform; 13.4. Lambda-bracket of local formal distributions; Lecture 14; 14.1. Completion of U, restricted representations and quantum fields 14.2. Normal ordered product |
| Record Nr. | UNINA-9910779990203321 |
Kac Victor G. <1943->
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Bombay lectures on highest weight representations of infinite dimensional lie algebras
| Bombay lectures on highest weight representations of infinite dimensional lie algebras |
| Autore | Kac Victor G. <1943-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, N.J., : World Scientific, 2013 |
| Descrizione fisica | 1 online resource (xii, 237 pages) |
| Disciplina | 520 |
| Collana |
Advanced series in mathematical physics
Gale eBooks |
| Soggetto topico |
Infinite dimensional Lie algebras
Quantum field theory |
| ISBN | 981-4522-20-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Preface to the second edition; CONTENTS; Lecture 1; 1.1. The Lie algebra d of complex vector fields on the circle; 1.2. Representations Vα,β of; 1.3. Central extensions of : the Virasoro algebra; Lecture 2; 2.1. Definition of positive-energy representations of Vir; 2.2. Oscillator algebra A; 2.3. Oscillator representations of Vir; Lecture 3; 3.1. Complete reducibility of the oscillator representations of Vir; 3.2. Highest weight representations of Vir; 3.3. Verma representations M(c, h) and irreducible highest weight representations V (c, h) of Vir
11.3. A character identity Lecture 12; 12.1. Preliminaries on sl2; 12.2. A tensor product decomposition of some representations of sl2; 12.3. Construction and unitarity of the discrete series representations of Vir; 12.4. Completion of the proof of the Kac determinant formula; 12.5. On non-unitarity in the region 0 c < 1, h 0; Lecture 13; 13.1. Formal distributions; 13.2. Local pairs of formal distributions; 13.3. Formal Fourier transform; 13.4. Lambda-bracket of local formal distributions; Lecture 14; 14.1. Completion of U, restricted representations and quantum fields 14.2. Normal ordered product |
| Record Nr. | UNINA-9910814425703321 |
|
Kac Victor G. <1943->
|
||
| Singapore ; ; Hackensack, N.J., : World Scientific, 2013 | ||
| 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 |
| 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 | ||
| ||
Differential topology, infinite-dimensional lie algebras, and applications : D. B. Fuchs' 60th anniversary collection / Alexander Astashkevich, Serge Tabachnikov, editors
| Differential topology, infinite-dimensional lie algebras, and applications : D. B. Fuchs' 60th anniversary collection / Alexander Astashkevich, Serge Tabachnikov, editors |
| Autore | Astashkevich, Alexander |
| Pubbl/distr/stampa | Providence, R.I. : American Mathematical Society, c1999 |
| Descrizione fisica | x, 313 p. : ill. ; 26 cm |
| Disciplina | 514.74 |
| Altri autori (Persone) | Tabachnikov, Sergeauthor |
| Collana |
Advances in the mathematical sciences ; 44
American Mathematical Society Translations, 0065-9290 ; Ser.2, v.194 |
| Soggetto topico |
Differential topology
Infinite dimensional Lie algebras |
| ISBN | 082182032X |
| Classificazione | AMS 58-06 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000824009707536 |
|
Astashkevich, Alexander
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| Providence, R.I. : American Mathematical Society, c1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Elliptic genera and vertex operator super-algebras / / Hirotaka Tamanoi
| Elliptic genera and vertex operator super-algebras / / Hirotaka Tamanoi |
| Autore | Tamanoi Hirotaka <1958-> |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1999] |
| Descrizione fisica | 1 online resource (VIII, 396 p.) |
| Disciplina | 512.55 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Riemannian manifolds
Representations of algebras Infinite dimensional Lie algebras |
| ISBN | 3-540-48788-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | and summary of results -- Elliptic genera -- Vertex operator super algebras -- G-invariant vertex operator super subalgebras -- Geometric structure in vector spaces and reduction of structure groups on manifolds -- Infinite dimensional symmetries in elliptic genera for Kähler manifolds. |
| Record Nr. | UNINA-9910146308203321 |
|
Tamanoi Hirotaka <1958->
|
||
| Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1999] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elliptic genera and vertex operator super-algebras / / Hirotaka Tamanoi
| Elliptic genera and vertex operator super-algebras / / Hirotaka Tamanoi |
| Autore | Tamanoi Hirotaka <1958-> |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1999] |
| Descrizione fisica | 1 online resource (VIII, 396 p.) |
| Disciplina | 512.55 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Riemannian manifolds
Representations of algebras Infinite dimensional Lie algebras |
| ISBN | 3-540-48788-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | and summary of results -- Elliptic genera -- Vertex operator super algebras -- G-invariant vertex operator super subalgebras -- Geometric structure in vector spaces and reduction of structure groups on manifolds -- Infinite dimensional symmetries in elliptic genera for Kähler manifolds. |
| Record Nr. | UNISA-996466616403316 |
|
Tamanoi Hirotaka <1958->
|
||
| Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1999] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Extended affine Lie algebras and their root systems / / Bruce N. Allison [and four others]
| Extended affine Lie algebras and their root systems / / Bruce N. Allison [and four others] |
| Autore | Allison Bruce N (Bruce Normansell), <1945-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1997] |
| Descrizione fisica | 1 online resource (138 p.) |
| Disciplina |
510 s
512/.55 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Infinite dimensional Lie algebras
Kac-Moody algebras Root systems (Algebra) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0188-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910480216803321 |
|
Allison Bruce N (Bruce Normansell), <1945->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1997] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Extended affine Lie algebras and their root systems / / Bruce N. Allison [and four others]
| Extended affine Lie algebras and their root systems / / Bruce N. Allison [and four others] |
| Autore | Allison Bruce N (Bruce Normansell), <1945-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1997] |
| Descrizione fisica | 1 online resource (138 p.) |
| Disciplina |
510 s
512/.55 |
| Altri autori (Persone) | AllisonBruce N <1945-> (Bruce Normansell) |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Infinite dimensional Lie algebras
Kac-Moody algebras Root systems (Algebra) |
| ISBN | 1-4704-0188-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910788731603321 |
|
Allison Bruce N (Bruce Normansell), <1945->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1997] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
