By Bruce Allison, John Faulkner (auth.), Karl-Hermann Neeb, Arturo Pianzola (eds.)

ISBN-10: 0817647406

ISBN-13: 9780817647407

ISBN-10: 0817647414

ISBN-13: 9780817647414

This number of invited expository articles makes a speciality of fresh advancements and traits in infinite-dimensional Lie thought, which has turn into one of many center parts of contemporary arithmetic. The booklet is split into 3 components: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) teams, and illustration idea of infinite-dimensional Lie groups.

Part (A) is especially serious about the constitution and illustration idea of infinite-dimensional Lie algebras and comprises articles at the constitution of direct-limit Lie algebras, prolonged affine Lie algebras and loop algebras, in addition to representations of loop algebras and Kac–Moody superalgebras.

The articles partially (B) learn connections among infinite-dimensional Lie idea and geometry. the themes diversity from infinite-dimensional teams performing on fiber bundles, corresponding attribute sessions and gerbes, to Jordan-theoretic geometries and new effects on direct-limit groups.

The analytic illustration idea of infinite-dimensional Lie teams continues to be greatly underdeveloped. The articles partially (C) strengthen new, promising tools in line with warmth kernels, multiplicity freeness, Banach–Lie–Poisson areas, 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, ok. Styrkas, ok. Waldorf, and J.A. Wolf.