000			04046nam a22006017a 4500
001			sulb-eb0024660
003			BD-SySUS
005			20160413122451.0
007			cr nn 008mamaa
008			130228s2013 gw | s |||| 0|eng d
020			_a9783642362163 _9978-3-642-36216-3
024	7		_a10.1007/978-3-642-36216-3 _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		_aMeinrenken, Eckhard. _eauthor.
245	1	0	_aClifford Algebras and Lie Theory _h[electronic resource] / _cby Eckhard Meinrenken.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013.
300			_aXX, 321 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, _x0071-1136 ; _v58
505	0		_aPreface -- Conventions -- List of Symbols -- 1 Symmetric bilinear forms -- 2 Clifford algebras -- 3 The spin representation -- 4 Covariant and contravariant spinors -- 5 Enveloping algebras -- 6 Weil algebras -- 7 Quantum Weil algebras -- 8 Applications to reductive Lie algebras -- 9 D(g; k) as a geometric Dirac operator -- 10 The Hopf–Koszul–Samelson Theorem -- 11 The Clifford algebra of a reductive Lie algebra -- A Graded and filtered super spaces -- B Reductive Lie algebras -- C Background on Lie groups -- References -- Index.
520			_aThis monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.
650		0	_aMathematics.
650		0	_aAssociative rings.
650		0	_aRings (Algebra).
650		0	_aTopological groups.
650		0	_aLie groups.
650		0	_aMathematical physics.
650		0	_aDifferential geometry.
650		0	_aPhysics.
650	1	4	_aMathematics.
650	2	4	_aTopological Groups, Lie Groups.
650	2	4	_aAssociative Rings and Algebras.
650	2	4	_aMathematical Applications in the Physical Sciences.
650	2	4	_aDifferential Geometry.
650	2	4	_aMathematical Methods in Physics.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642362156
830		0	_aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, _x0071-1136 ; _v58
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-36216-3
912			_aZDB-2-SMA
942			_2Dewey Decimal Classification _ceBooks
999			_c46752 _d46752