The Resource Clifford algebras and lie theory, Eckhard Meinrenken
Clifford algebras and lie theory, Eckhard Meinrenken
Resource Information
The item Clifford algebras and lie theory, Eckhard Meinrenken represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Clifford algebras and lie theory, Eckhard Meinrenken represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource.
- 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
- Isbn
- 9783642362163
- Label
- Clifford algebras and lie theory
- Title
- Clifford algebras and lie theory
- Statement of responsibility
- Eckhard Meinrenken
- Subject
-
- Associative Rings and Algebras.
- Clifford algebras
- Clifford algebras
- Clifford algebras
- Clifford-Algebra
- Differential Geometry.
- Global differential geometry.
- Lie algebras
- Lie algebras
- Lie algebras
- Lie-Algebra
- Mathematical Applications in the Physical Sciences.
- Mathematical physics.
- Mathematics.
- Topological Groups, Lie Groups.
- Topological Groups.
- Algebra.
- 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
- 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
- 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
- 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
Subject
- Associative Rings and Algebras.
- Clifford algebras
- Clifford algebras
- Clifford algebras
- Clifford-Algebra
- Differential Geometry.
- Global differential geometry.
- Lie algebras
- Lie algebras
- Lie algebras
- Lie-Algebra
- Mathematical Applications in the Physical Sciences.
- Mathematical physics.
- Mathematics.
- Topological Groups, Lie Groups.
- Topological Groups.
- Algebra.
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Clifford-algebras-and-lie-theory-Eckhard/xfLyb1AlRS0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Clifford-algebras-and-lie-theory-Eckhard/xfLyb1AlRS0/">Clifford algebras and lie theory, Eckhard Meinrenken</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
