Clifford Algebras and Lie Theory

• Κύριος συγγραφέας: Meinrenken, Eckhard (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Σειρά: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 58
• Θέματα: Mathematics.; Associative rings.; Rings (Algebra).; Topological groups.; Lie groups.; Mathematical physics.; Differential geometry.; Physics.; Topological Groups, Lie Groups.; Associative Rings and Algebras.; Mathematical Applications in the Physical Sciences.; Differential Geometry.; Mathematical Methods in Physics.

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...

Πίνακας περιεχομένων:

• 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.