An Introduction to Kac–Moody Groups over Fields
Timothée Marquis
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
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| FrontmatterDownload pp. i–v | |
| PrefaceDownload pp. vii–viii | |
| ContentsDownload pp. ix–xi | |
| IntroductionDownload pp. 1–11 | |
| Part I A few words on the classical Lie theoryp. 13 | |
| 1 | From Lie groups to Lie algebraspp. 15–17 |
| 2 | Finite-dimensional (real or complex) Lie algebraspp. 19–34 |
| Part II Kac–Moody algebrasp. 35 | |
| 3 | Basic definitionspp. 37–55 |
| 4 | TheWeyl group of a Kac–Moody algebrapp. 57–74 |
| 5 | Kac–Moody algebras of finite and affine typepp. 75–88 |
| 6 | Real and imaginary rootspp. 89–96 |
| Part III Kac–Moody groupsp. 97 | |
| PrologueDownload p. 99 | |
| 7 | Minimal Kac–Moody groupspp. 101–171 |
| 8 | Maximal Kac–Moody groupspp. 173–268 |
| 9 | Loose endspp. 269–276 |
| A | Group schemespp. 277–287 |
| B | Buildings and BN-pairspp. 289–314 |
| Bibliographypp. 315–320 | |
| Indexpp. 321–323 | |
| Index of symbolspp. 325–331 |