Clifford Algebras and Lie Theory by Eckhard Meinrenken (English) Hardcover Book

Description: 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher 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 Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petraccis 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 Duflos theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostants 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. Author Biography 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 Preface.- Conventions.- List of Symbols.- 1 Symmetric bilinear forms.- 2 Clifford algebras.- 3 The spin representation.- 4 Covariant and contravariant spinors.- 5 Enveloping algebras.- 6 Weil algebras.- 7 Quantum Weil algebras.- 8 Applications to reductive Lie algebras.- 9 D(g; k) as a geometric Dirac operator.- 10 The Hopf–Koszul–Samelson Theorem.- 11 The Clifford algebra of a reductive Lie algebra.- A Graded and filtered super spaces.- B Reductive Lie algebras.- C Background on Lie groups.- References.- Index. Feature 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 authors research Largely self-contained exposition Details ISBN364236215X Author Eckhard Meinrenken Short Title CLIFFORD ALGEBRAS & LIE THEORY Language English ISBN-10 364236215X ISBN-13 9783642362156 Media Book Format Hardcover Series Number 58 Year 2013 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 512.57 Pages 321 Edition 2013th DOI 10.1007/978-3-642-36216-3 UK Release Date 2013-03-16 Publication Date 2013-03-16 Illustrations XX, 321 p. Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2013 ed. Series Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Alternative 9783642436697 Audience Undergraduate We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96289136;

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