Coverart for item
The Resource Clifford algebras and lie theory, Eckhard Meinrenken

Clifford algebras and lie theory, Eckhard Meinrenken

Label
Clifford algebras and lie theory
Title
Clifford algebras and lie theory
Statement of responsibility
Eckhard Meinrenken
Creator
Subject
Language
eng
Summary
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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Meinrenken, Eckhard
Dewey number
512/.57
Index
index present
LC call number
QA199
LC item number
.M45 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge,
Series volume
v. 58
http://library.link/vocab/subjectName
  • Clifford algebras
  • Lie algebras
  • Clifford algebras
  • Lie algebras
  • Clifford-Algebra
  • Lie-Algebra
Label
Clifford algebras and lie theory, Eckhard Meinrenken
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • as a geometric Dirac operator
  • The Hopf-Koszul-Samelson Theorem
  • The Clifford algebra of a reductive Lie algebra
  • Symmetric bilinear forms
  • Clifford algebras
  • The spin representation
  • Covariant and contravariant spinors
  • Enveloping algebras
  • Weil algebras
  • Quantum Weil algebras
  • Applications to reductive Lie algebras
Control code
829740609
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783642362163
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-642-36216-3
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)829740609
Label
Clifford algebras and lie theory, Eckhard Meinrenken
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • as a geometric Dirac operator
  • The Hopf-Koszul-Samelson Theorem
  • The Clifford algebra of a reductive Lie algebra
  • Symmetric bilinear forms
  • Clifford algebras
  • The spin representation
  • Covariant and contravariant spinors
  • Enveloping algebras
  • Weil algebras
  • Quantum Weil algebras
  • Applications to reductive Lie algebras
Control code
829740609
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783642362163
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-642-36216-3
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)829740609

Library Locations

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      38.944491 -92.326012
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