000 | 04421nam a22005775i 4500 | ||
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001 | 978-0-8176-4741-4 | ||
003 | DE-He213 | ||
005 | 20140220083711.0 | ||
007 | cr nn 008mamaa | ||
008 | 101029s2011 xxu| s |||| 0|eng d | ||
020 |
_a9780817647414 _9978-0-8176-4741-4 |
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024 | 7 |
_a10.1007/978-0-8176-4741-4 _2doi |
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050 | 4 | _aQA252.3 | |
050 | 4 | _aQA387 | |
072 | 7 |
_aPBG _2bicssc |
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072 | 7 |
_aMAT014000 _2bisacsh |
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072 | 7 |
_aMAT038000 _2bisacsh |
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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. |
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300 |
_aVIII, 492p. 9 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aProgress in Mathematics ; _v288 |
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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 |