LEADER 05060nam 22008655 450 001 9910739481703321 005 20200706173020.0 010 $a3-642-36216-8 024 7 $a10.1007/978-3-642-36216-3 035 $a(CKB)2670000000360686 035 $a(EBL)1206113 035 $a(SSID)ssj0000878612 035 $a(PQKBManifestationID)11500334 035 $a(PQKBTitleCode)TC0000878612 035 $a(PQKBWorkID)10836476 035 $a(PQKB)10693970 035 $a(DE-He213)978-3-642-36216-3 035 $a(MiAaPQ)EBC6314878 035 $a(MiAaPQ)EBC1206113 035 $a(Au-PeEL)EBL1206113 035 $a(CaPaEBR)ebr10983214 035 $a(OCoLC)845259482 035 $a(PPN)168329905 035 $a(EXLCZ)992670000000360686 100 $a20130228d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aClifford Algebras and Lie Theory /$fby Eckhard Meinrenken 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (321 p.) 225 1 $aErgebnisse der Mathematik und ihrer Grezgebiete. ;$v3. Folge, Volume 58 300 $aOriginally published: 2013. 311 $a3-642-43669-2 311 $a3-642-36215-X 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan?s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci?s proof of the Poincaré?Birkhoff?Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo?s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant?s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his ?Clifford algebra analogue? of the Hopf?Koszul?Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics. 410 0$aErgebnisse der Mathematik und ihrer Grezgebiete. ;$v3. Folge, Bd. 58. 606 $aTopological groups 606 $aLie groups 606 $aAssociative rings 606 $aRings (Algebra) 606 $aMathematical physics 606 $aDifferential geometry 606 $aPhysics 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 615 0$aTopological groups. 615 0$aLie groups. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 0$aMathematical physics. 615 0$aDifferential geometry. 615 0$aPhysics. 615 14$aTopological Groups, Lie Groups. 615 24$aAssociative Rings and Algebras. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aDifferential Geometry. 615 24$aMathematical Methods in Physics. 676 $a512.57 700 $aMeinrenken$b Eckhard$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521474 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910739481703321 996 $aClifford algebras and Lie theory$9836950 997 $aUNINA