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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 Duflös 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.
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 Duflös 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.
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.
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 author's research
Largely self-contained exposition
Includes supplementary material: [...]
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.
| Erscheinungsjahr: | 2013 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 344 |
| Reihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Inhalt: |
xx
321 S. |
| ISBN-13: | 9783642362156 |
| ISBN-10: | 364236215X |
| Sprache: | Englisch |
| Herstellernummer: | 86146449 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Meinrenken, Eckhard |
| Auflage: | 2013 |
| Hersteller: |
Springer-Verlag GmbH
Springer Berlin Heidelberg Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Maße: | 241 x 160 x 24 mm |
| Von/Mit: | Eckhard Meinrenken |
| Erscheinungsdatum: | 16.03.2013 |
| Gewicht: | 0,682 kg |
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.
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 author's research
Largely self-contained exposition
Includes supplementary material: [...]
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.
| Erscheinungsjahr: | 2013 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 344 |
| Reihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Inhalt: |
xx
321 S. |
| ISBN-13: | 9783642362156 |
| ISBN-10: | 364236215X |
| Sprache: | Englisch |
| Herstellernummer: | 86146449 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Meinrenken, Eckhard |
| Auflage: | 2013 |
| Hersteller: |
Springer-Verlag GmbH
Springer Berlin Heidelberg Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics |
| Maße: | 241 x 160 x 24 mm |
| Von/Mit: | Eckhard Meinrenken |
| Erscheinungsdatum: | 16.03.2013 |
| Gewicht: | 0,682 kg |
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