Clifford Algebras and Lie Theory

Clifford Algebras and Lie Theory English | 341 pages | ISBN-10: 364236215X | PDF | 4,31 MB 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 Poincare–Birkhoff–Witt theorem.