Clifford Algebras and Lie Theory by Eckhard Meinrenken

Clifford Algebras and Lie Theory by Eckhard Meinrenken

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.

Main areas of research are symplectic geometry, with applications to Lie theory and mathematical physics. 

Professor at the University of Toronto since 1998.

Honors include: Fellowship of the Royal Society of Canada (since 2008), Steacie Fellowship (2007), McLean Award (2003), Andre Aisenstadt Prize (2001).

Invited speaker at the 2002 ICM in Beijing.

SKU	Unavailable
ISBN 13	9783642362156
ISBN 10	364236215X
Title	Clifford Algebras and Lie Theory
Author	Eckhard Meinrenken
Series	Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge A Series Of Modern Surveys In Mathematics
Condition	Unavailable
Publisher	Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Year published	2013-03-16
Number of pages	321
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.