Clifford algebras and lie theory
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The work Clifford algebras and lie theory represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Clifford algebras and lie theory
Resource Information
The work Clifford algebras and lie theory represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Clifford algebras and lie theory
 Statement of responsibility
 Eckhard Meinrenken
 Subject

 Associative Rings and Algebras.
 Clifford algebras
 Clifford algebras
 Clifford algebras
 CliffordAlgebra
 Differential Geometry.
 Global differential geometry.
 Lie algebras
 Lie algebras
 Lie algebras
 LieAlgebra
 Mathematical Applications in the Physical Sciences.
 Mathematical physics.
 Mathematics.
 Topological Groups, Lie Groups.
 Topological Groups.
 Algebra.
 Language
 eng
 Summary
 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 Cartan's famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci's proof of the PoincarĂ©BirkhoffWitt theorem. This is followed by discussions of Weil algebras, ChernWeil 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 HopfKoszulSamelson theorem, and explains his fascinating conjecture relating the HarishChandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and uptodate reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics
 Cataloging source
 GW5XE
 Dewey number
 512/.57
 Index
 index present
 LC call number
 QA199
 LC item number
 .M45 2013
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge,
 Series volume
 v. 58
Context
Context of Clifford algebras and lie theoryWork of
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