Clifford Algebras and Lie Theory

• Main Author: Meinrenken, Eckhard. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 58
• Subjects: Mathematics.; Algebra.; Topological Groups.; Global differential geometry.; Mathematical physics.; Topological Groups, Lie Groups.; Associative Rings and Algebras.; Mathematical Applications in the Physical Sciences.; Differential Geometry.; Mathematical Methods in Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-36216-3

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 gro...

Table of Contents:

• 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<U+0013>Koszul<U+0013>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.