INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783642362163
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52327
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Clifford Algebras and Lie Theor
General Material Designation
[Book]
Other Title Information
:[delta
First Statement of Responsibility
/ by Eckhard Meinrenken
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Berlin, Heidelberg
Name of Publisher, Distributor, etc.
: Springer Berlin Heidelberg :Imprint: Springer,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XX, 321 p., online resource.
SERIES
Series Title
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136
Volume Designation
; 58)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
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 Poincar?ش-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.
Text of Note
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.?╗╣
SERIES
Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,0071-1136
Volume Number
58
TOPICAL NAME USED AS SUBJECT
Mathematics
Algebra
Topological Groups
Global differential geometry
Mathematical physics
Electronic books
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Meinrenken, Eckhard.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9783642362156.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9783642362156.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
