9783642544668-3642544665-Clifford Algebras and Lie Theory (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a)

Clifford Algebras and Lie Theory (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a)

ISBN-13: 9783642544668
ISBN-10: 3642544665
Edition: 2013
Author: Meinrenken, Eckhard
Publication date: 2014
Publisher: Springer
Format: Paperback 341 pages
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Book details

ISBN-13: 9783642544668
ISBN-10: 3642544665
Edition: 2013
Author: Meinrenken, Eckhard
Publication date: 2014
Publisher: Springer
Format: Paperback 341 pages

Summary

Acknowledged authors Meinrenken, Eckhard wrote Clifford Algebras and Lie Theory (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a) comprising 341 pages back in 2014. Textbook and eTextbook are published under ISBN 3642544665 and 9783642544668. Since then Clifford Algebras and Lie Theory (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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.

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