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Catalogue Information
Field name	Details
Dewey Class	512.55
Dewey Class	512.482
Title	Clifford Algebras and Lie Theory ([Ebook]) / by Eckhard Meinrenken.
Author	Meinrenken, Eckhard
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer
Publication	, 2013.
Physical Details	XX, 321 pages : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 0071-1136 ; ; 58
ISBN	9783642362163
Summary Note	This 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 Cartanâs famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracciâs 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 Dufloâs theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostantâs structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his âClifford algebra analogueâ 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.:
Contents note	Preface -- 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-36216-3
Links to Related Works	Subject References: Algebra . Clifford algebras . Differential Geometry . Global differential geometry . Lie algebras . Mathematical Methods in Physics . Mathematical Physics . Topological groups . Authors: Meinrenken, Eckhard . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics . Classification: 512.482 . 512.55 . 512.55 (DDC 23) .

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Clifford Algebras and Lie Theory

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