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Birkhäuser - Birkhäuser Mathematics | Developments and Trends in Infinite-Dimensional Lie Theory

Developments and Trends in Infinite-Dimensional Lie Theory

Series: Progress in Mathematics, Vol. 288

Neeb, Karl-Hermann, Pianzola, Arturo (Eds.)

2011, VIII, 492p. 9 illus..

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  • 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

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.

Content Level » Research

Keywords » Kac--Moody superalgebras - direct limit groups - heat kernels - loop algebras - multiplicity freeness

Related subjects » Birkhäuser Mathematics

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