Clifford algebras and lie theory
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 gro...
Enregistré dans:
| Hovedforfatter: | |
|---|---|
| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer
[20..].
Cham : Springer Nature |
| Serier: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
58 |
| Fag: | |
| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Kommentar: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Clifford algebras and Lie theory, Eckhard Meinrenken, 2013, Berlin, Springer, 1 vol. (XX-321 p.), Ergebnisse der Mathematik und ihrer Grenzgebiete, 978-3-642-36215-6 |
| 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 |
|---|---|
| Emne beskrivelse: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783642362163 |
| ISSN: | 0071-1136 |
| Adgang: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |