Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Clifford Algebras and Lie Theory

Authors: Meinrenken, Eckhard

  • Convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics
  • Included are many developments from the last 15 years, drawn in part from the author's research
  • Largely self-contained exposition
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About this Textbook

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.

About the authors

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.

Table of contents (11 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-36216-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-36215-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA
  • ISBN 978-3-642-54466-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Clifford Algebras and Lie Theory
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
58
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-36216-3
DOI
10.1007/978-3-642-36216-3
Hardcover ISBN
978-3-642-36215-6
Softcover ISBN
978-3-642-54466-8
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XX, 321
Topics