Developments and trends in infinite-dimensional Lie theory
著者
書誌事項
Developments and trends in infinite-dimensional Lie theory
（Progress in mathematics, v. 288）
Birkhäuser , Springer, c2011
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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. Gloeckner, 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.
目次
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.
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