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001 978-0-8176-4741-4
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007 cr nn 008mamaa
008 101029s2011 xxu| s |||| 0|eng d
020 _a9780817647414
_9978-0-8176-4741-4
024 7 _a10.1007/978-0-8176-4741-4
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aMAT038000
_2bisacsh
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aNeeb, Karl-Hermann.
_eeditor.
245 1 0 _aDevelopments and Trends in Infinite-Dimensional Lie Theory
_h[electronic resource] /
_cedited by Karl-Hermann Neeb, Arturo Pianzola.
264 1 _aBoston :
_bBirkhäuser Boston,
_c2011.
300 _aVIII, 492p. 9 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics ;
_v288
505 0 _aPreface -- 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.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGeometry, algebraic.
650 0 _aGroup theory.
650 0 _aTopological Groups.
650 0 _aGeometry.
650 1 4 _aMathematics.
650 2 4 _aTopological Groups, Lie Groups.
650 2 4 _aGroup Theory and Generalizations.
650 2 4 _aAlgebra.
650 2 4 _aGeometry.
650 2 4 _aAlgebraic Geometry.
700 1 _aPianzola, Arturo.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817647407
830 0 _aProgress in Mathematics ;
_v288
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-4741-4
912 _aZDB-2-SMA
999 _c105082
_d105082