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001			EBC3114048
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005			20240729124558.0
006			m o d |
007			cr cnu||||||||
008			240724s2009 xx o ||||0 eng d
020			_a9781470405304 _q(electronic bk.)
020			_z9780821842584
035			_a(MiAaPQ)EBC3114048
035			_a(Au-PeEL)EBL3114048
035			_a(CaPaEBR)ebr11039667
035			_a(OCoLC)922981573
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA174.2 -- .C37 2009eb
082	0		_a511.3/26
100	1		_aCaprace, Pierre-Emmanuel.
245	1	0	_aAbstract' Homomorphisms of Split Kac-Moody Groups.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2009.
264		4	_c©2009.
300			_a1 online resource (108 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.198
505	0		_aIntro -- Contents -- Introduction -- Acknowledgements -- Chapter 1. The objects: Kac-Moody groups, root data and Tits buildings -- 1.1. Kac-Moody groups and Tits functors -- 1.2. Root data -- 1.3. Tits buildings -- 1.4. Twin root data and twin buildings: a short dictionary -- Chapter 2. Basic tools from geometric group theory -- 2.1. CAT(0) geometry -- 2.2. Rigidity of algebraic-group-actions on trees -- Chapter 3. Kac-Moody groups and algebraic groups -- 3.1. Bounded subgroups -- 3.2. Adjoint representation of Tits functors -- 3.3. A few facts from the theory of algebraic groups -- Chapter 4. Isomorphisms of Kac-Moody groups: an overview -- 4.1. The isomorphism theorem -- 4.2. Diagonalizable subgroups and their centralizers -- 4.3. Completely reducible subgroups and their centralizers -- 4.4. Basic recognition of the ground field -- 4.5. Detecting rank one subgroups of Kac-Moody groups -- 4.6. Images of diagonalizable subgroups under Kac-Moody group isomorphisms -- 4.7. A technical auxiliary to the isomorphism theorem -- Chapter 5. Isomorphisms of Kac-Moody groups in characteristic zero -- 5.1. Rigidity of SL[sub(2)](Q)-actions on CAT(0) polyhedral complexes -- 5.2. Homomorphisms of Chevalley groups over Q to Kac-Moody groups -- 5.3. Regularity of diagonalizable subgroups -- 5.4. Proof of the isomorphism theorem -- Chapter 6. Isomorphisms of Kac-Moody groups in positive characteristic -- 6.1. On bounded subgroups of Kac-Moody groups -- 6.2. Homomorphisms of certain algebraic groups to Kac-Moody groups -- 6.3. Images of certain small subgroups under Kac-Moody group isomorphisms -- 6.4. Proof of the isomorphism theorem -- Chapter 7. Homomorphisms of Kac-Moody groups to algebraic groups -- 7.1. The non-linearity theorem -- 7.2. A combinatorial characterization of affine Coxeter groups -- 7.3. On infinite root systems.
505	8		_a7.4. Proof of the non-linearity theorem -- Chapter 8. Unitary forms of Kac-Moody groups -- 8.1. Introduction -- 8.2. Definitions -- 8.3. Isomorphisms of unitary forms -- 8.4. Non-linearity -- Bibliography -- Index -- A -- B -- C -- D -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aIsomorphisms (Mathematics).
650		0	_aAutomorphisms.
650		0	_aKac-Moody algebras.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aCaprace, Pierre-Emmanuel _tAbstract' Homomorphisms of Split Kac-Moody Groups _dProvidence : American Mathematical Society,c2009 _z9780821842584
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114048 _zClick to View
999			_c69579 _d69579