Download EBOOK Clifford Algebras and Lie Theory PDF for free
 
Category: Science & Geography
The author of the book: Eckhard Meinrenken
Format files: PDF, EPUB, TXT, DOCX
The size of the: 4.90 MB
Language: English
ISBN13: 9783642362156
Edition: SpringerVerlag Berlin and Heidelberg GmbH & Co. K
Date of issue: 16 March 2013

Description of the book "Clifford Algebras and Lie Theory":
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 PoincareBirkhoffWitt theorem. This is followed by discussions of Weil algebras, ChernWeil theory, the quantum Weil algebra, and the PDF 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 HopfKoszulSamelson theorem, and explains his fascinating conjecture relating the HarishChandra projection for Clifford algebras to the principal sl(2) subalgebra.
Aside from these beautiful applications, the book will serve as a convenient and uptodate reference for background material from Clifford ePub theory, relevant for students and researchers in mathematics and physics.
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Eckhard Meinrenken
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