Developments and Trends in Infinite-Dimensional Lie Theory

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. 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.

The distinguished contributors include: B. Allison, D. Beltita, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T. Ratiu, N. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J. Wolf.

Invited papers written by distinguished researchers Expository essays focus on recent developments and trends in infinite-dimensional Lie theory Discusses new methods, structures, and representations of infinite-dimensional Lie groups Includes supplementary material: sn.pub/extras

Contenu
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.- KacMoody 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.