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Developments and Trends in Infinite-Dimensional Lie Theory
This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor Corporativo: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston, MA :
Birkhäuser Boston : Imprint: Birkhäuser,
2011.
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| Edición: | 1st ed. 2011. |
| Colección: | Progress in Mathematics,
288 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-0-8176-4741-4 | ||
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| 245 | 1 | 0 | |a Developments and Trends in Infinite-Dimensional Lie Theory |h [electronic resource] / |c edited by Karl-Hermann Neeb, Arturo Pianzola. |
| 250 | |a 1st ed. 2011. | ||
| 264 | 1 | |a Boston, MA : |b Birkhäuser Boston : |b Imprint: Birkhäuser, |c 2011. | |
| 300 | |a VIII, 492 p. 9 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Progress in Mathematics, |x 2296-505X ; |v 288 | |
| 505 | 0 | |a Preface -- Part A: Infinite-Dimensional Lie (Super-)Algebras -- Isotopy for Extended Affine Lie Algebras and Lie Tori -- Remarks on the Isotriviality of Multiloop Algebras -- Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras - A Survey -- Tensor Representations of Classical Locally Finite Lie Algebras -- Lie Algebras, Vertex Algebras, and Automorphic Forms -- Kac-Moody Superalgebras and Integrability -- Part B: Geometry of Infinite-Dimensional Lie (Transformation) Groups -- Jordan Structures and Non-Associative Geometry -- Direct Limits of Infinite-Dimensional Lie Groups -- Lie Groups of Bundle Automorphisms and Their Extensions -- Gerbes and Lie Groups -- Part C: Representation Theory of Infinite-Dimensional Lie Groups Functional Analytic Background for a Theory of Infinite- Dimensional Reductive Lie Groups -- Heat Kernel Measures and Critical Limits -- Coadjoint Orbits and the Beginnings of a Geometric Representation Theory -- Infinite-Dimensional Multiplicity-Free Spaces I: Limits of Compact Commutative Spaces -- Index. | |
| 520 | |a This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac-Moody superalgebras. The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups. The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach-Lie-Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf. | ||
| 650 | 0 | |a Topological groups. | |
| 650 | 0 | |a Lie groups. | |
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Algebra. | |
| 650 | 0 | |a Geometry. | |
| 650 | 0 | |a Algebraic geometry. | |
| 650 | 1 | 4 | |a Topological Groups and Lie Groups. |
| 650 | 2 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Algebra. |
| 650 | 2 | 4 | |a Geometry. |
| 650 | 2 | 4 | |a Algebraic Geometry. |
| 700 | 1 | |a Neeb, Karl-Hermann. |e editor. |4 edt |4 http://id.loc.gov/vocabulary/relators/edt | |
| 700 | 1 | |a Pianzola, Arturo. |e editor. |4 edt |4 http://id.loc.gov/vocabulary/relators/edt | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9780817647407 |
| 776 | 0 | 8 | |i Printed edition: |z 9780817672331 |
| 830 | 0 | |a Progress in Mathematics, |x 2296-505X ; |v 288 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-0-8176-4741-4 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||