000 | 03714nam a22005175i 4500 | ||
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001 | 978-3-319-09773-2 | ||
003 | DE-He213 | ||
005 | 20190213151054.0 | ||
007 | cr nn 008mamaa | ||
008 | 141014s2014 gw | s |||| 0|eng d | ||
020 |
_a9783319097732 _9978-3-319-09773-2 |
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024 | 7 |
_a10.1007/978-3-319-09773-2 _2doi |
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050 | 4 | _aQA403-403.3 | |
072 | 7 |
_aPBKD _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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_aPBKD _2thema |
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082 | 0 | 4 |
_a515.785 _223 |
100 | 1 |
_aRouvière, François. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aSymmetric Spaces and the Kashiwara-Vergne Method _h[electronic resource] / _cby François Rouvière. |
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2014. |
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300 |
_aXXI, 196 p. _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 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2115 |
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505 | 0 | _aIntroduction -- Notation -- The Kashiwara-Vergne method for Lie groups -- Convolution on homogeneous spaces -- The role of e-functions -- e-functions and the Campbell Hausdorff formula -- Bibliography. | |
520 | _aGathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject. Its goal is to: - motivate and explain the method for general Lie groups, reducing the proof of deep results in invariant analysis to the verification of two formal Lie bracket identities related to the Campbell-Hausdorff formula (the "Kashiwara-Vergne conjecture"); - give a detailed proof of the conjecture for quadratic and solvable Lie algebras, which is relatively elementary; - extend the method to symmetric spaces; here an obstruction appears, embodied in a single remarkable object called an "e-function"; - explain the role of this function in invariant analysis on symmetric spaces, its relation to invariant differential operators, mean value operators and spherical functions; - give an explicit e-function for rank one spaces (the hyperbolic spaces); - construct an e-function for general symmetric spaces, in the spirit of Kashiwara and Vergne's original work for Lie groups. The book includes a complete rewriting of several articles by the author, updated and improved following Alekseev, Meinrenken and Torossian's recent proofs of the conjecture. The chapters are largely independent of each other. Some open problems are suggested to encourage future research. It is aimed at graduate students and researchers with a basic knowledge of Lie theory. | ||
650 | 0 | _aHarmonic analysis. | |
650 | 0 | _aGlobal differential geometry. | |
650 | 0 | _aAlgebra. | |
650 | 0 | _aGlobal analysis. | |
650 | 1 | 4 |
_aAbstract Harmonic Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M12015 |
650 | 2 | 4 |
_aDifferential Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M21022 |
650 | 2 | 4 |
_aNon-associative Rings and Algebras. _0http://scigraph.springernature.com/things/product-market-codes/M11116 |
650 | 2 | 4 |
_aGlobal Analysis and Analysis on Manifolds. _0http://scigraph.springernature.com/things/product-market-codes/M12082 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783319097749 |
776 | 0 | 8 |
_iPrinted edition: _z9783319097725 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2115 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-09773-2 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c9417 _d9417 |