Clifford Algebras and Lie Theory

Nonfiction, Science & Nature, Mathematics, Group Theory, Algebra
Cover of the book Clifford Algebras and Lie Theory by Eckhard Meinrenken, Springer Berlin Heidelberg
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Eckhard Meinrenken ISBN: 9783642362163
Publisher: Springer Berlin Heidelberg Publication: February 28, 2013
Imprint: Springer Language: English
Author: Eckhard Meinrenken
ISBN: 9783642362163
Publisher: Springer Berlin Heidelberg
Publication: February 28, 2013
Imprint: Springer
Language: English

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 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 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.

More books from Springer Berlin Heidelberg

Cover of the book Osteoarthritis by Eckhard Meinrenken
Cover of the book Environmental Finance and Investments by Eckhard Meinrenken
Cover of the book Myocarditis Cardiomyopathy by Eckhard Meinrenken
Cover of the book Echo-Planar Imaging by Eckhard Meinrenken
Cover of the book Dem Gutes tun, der leidet by Eckhard Meinrenken
Cover of the book Technologie von Unternehmenssoftware by Eckhard Meinrenken
Cover of the book Advances and Challenges in Space-time Modelling of Natural Events by Eckhard Meinrenken
Cover of the book Transport and Chemical Transformation in the Troposphere by Eckhard Meinrenken
Cover of the book Implementierung von IT Service-Management by Eckhard Meinrenken
Cover of the book Evaluating Water Projects by Eckhard Meinrenken
Cover of the book Behavioral Neurogenetics by Eckhard Meinrenken
Cover of the book Varicella-zoster Virus by Eckhard Meinrenken
Cover of the book Bioluminescence: Fundamentals and Applications in Biotechnology - Volume 2 by Eckhard Meinrenken
Cover of the book Varicella-Zoster Virus Epithelial Keratitis in Herpes Zoster Ophthalmicus by Eckhard Meinrenken
Cover of the book Natur für die Seele by Eckhard Meinrenken
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy