Developments and Trends in Infinite-dimensional Lie Theory

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2010-10-28
  • Publisher: Birkhauser

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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. Glckner, 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.

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