000			04023nam a22005655i 4500
003			DE-He213
005			20191014030959.0
007			cr nn 008mamaa
008			130228s2013 gw | s |||| 0|eng d
020	6	4	_a9783642362163 _9978-3-642-36216-3
024	8	7	_a10.1007/978-3-642-36216-3 _2doi
050	8	4	_aQA252.3
050	8	4	_aQA387
072	8	7	_aPBG _2bicssc
072	8	7	_aMAT014000 _2bisacsh
072	8	7	_aMAT038000 _2bisacsh
082			_a512.55 _223
082			_a512.482 _223
100	8	1	_aMeinrenken, Eckhard. _eauthor. _9205306
245	9	7	_aClifford Algebras and Lie Theory _h[electronic resource] / _cby Eckhard Meinrenken.
001			000073804
300	6	4	_aXX, 321 p. _bonline resource.
490	8	1	_aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, _x0071-1136 ; _v58
505	8	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 HopfKoszulSamelson 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	6	4	_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 Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petraccis proof of the PoincarȨBirkhoffWitt 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 Duflos theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his ǣClifford algebra analogueǥ of the HopfKoszulSamelson 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	8	0	_aMathematics. _98571
650	8	0	_aAlgebra. _9160
650	8	0	_aTopological Groups. _99529
650	8	0	_aGlobal differential geometry. _99530
650	8	0	_aMathematical physics. _99251
650			_aMathematics. _98571
650			_aTopological Groups, Lie Groups. _99531
650			_aAssociative Rings and Algebras. _921561
650			_aMathematical Applications in the Physical Sciences. _933406
650			_aDifferential Geometry. _99532
650			_aMathematical Methods in Physics. _99252
710	8	2	_aSpringerLink (Online service) _9205307
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783642362156
830	8	0	_aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, _x0071-1136 ; _v58 _9205308
856			_uhttp://dx.doi.org/10.1007/978-3-642-36216-3 _zde clik aquí para ver el libro electrónico
264	8	1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2013.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
999			_c73534 _d73534
942			_c05