The Resource Clifford Algebras and Lie Theory, by Eckhard Meinrenken, (electronic resource)

Clifford Algebras and Lie Theory, by Eckhard Meinrenken, (electronic resource)

Label
Clifford Algebras and Lie Theory
Title
Clifford Algebras and Lie Theory
Statement of responsibility
by Eckhard Meinrenken
Creator
Author
Author
Subject
Language
  • eng
  • 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
http://library.link/vocab/creatorName
Meinrenken, Eckhard
Dewey number
512.57
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
T4HQAJK9CNc
Language note
English
LC call number
  • QA252.3
  • QA387
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,
Series volume
58
http://library.link/vocab/subjectName
  • Topological Groups
  • Algebra
  • Global differential geometry
  • Mathematical physics
  • Topological Groups, Lie Groups
  • Associative Rings and Algebras
  • Mathematical Applications in the Physical Sciences
  • Differential Geometry
  • Mathematical Methods in Physics
Label
Clifford Algebras and Lie Theory, by Eckhard Meinrenken, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (321 p.)
Form of item
online
Isbn
9783642362163
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-642-36216-3
Specific material designation
remote
System control number
  • (CKB)2670000000360686
  • (EBL)1206113
  • (SSID)ssj0000878612
  • (PQKBManifestationID)11500334
  • (PQKBTitleCode)TC0000878612
  • (PQKBWorkID)10836476
  • (PQKB)10693970
  • (DE-He213)978-3-642-36216-3
  • (EXLCZ)992670000000360686
Label
Clifford Algebras and Lie Theory, by Eckhard Meinrenken, (electronic resource)
Publication
Note
Description based upon print version of record
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2013.
Extent
1 online resource (321 p.)
Form of item
online
Isbn
9783642362163
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-642-36216-3
Specific material designation
remote
System control number
  • (CKB)2670000000360686
  • (EBL)1206113
  • (SSID)ssj0000878612
  • (PQKBManifestationID)11500334
  • (PQKBTitleCode)TC0000878612
  • (PQKBWorkID)10836476
  • (PQKB)10693970
  • (DE-He213)978-3-642-36216-3
  • (EXLCZ)992670000000360686

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