Developments and Trends in Infinite-Dimensional Lie Theory
(Sprache: Englisch)
This collection of invited expository papers focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.
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This collection of invited expository papers focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.
Klappentext zu „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 Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups.
Contributors: B. Allison, D. Beltita, 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.
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. Belti??, 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.
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. Belti??, 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.
Inhaltsverzeichnis zu „Developments and Trends in Infinite-Dimensional Lie Theory “
- 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
Bibliographische Angaben
- 2010, 492 Seiten, Maße: 16,3 x 24,3 cm, Gebunden, Englisch
- Ed. by Karl-Hermann Neeb and Arturo Pianzola
- Herausgegeben: Karl-Hermann Neeb, Arturo Pianzola
- Verlag: Springer
- ISBN-10: 0817647406
- ISBN-13: 9780817647407
Sprache:
Englisch
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