7 Root systems and root lattices

Kapitel in diesem Buch

1. Frontmatter i
2. Contents iii
3. Preface vii
4. 1 Introduction 1
5. 2 Group action. Basic definitions and examples 5
6. 3 Delone sets and periodic lattices 25
7. 4 Lattice symmetry 43
8. 5 Lattices and their Voronoï and Delone cells 81
9. 6 Lattices and positive quadratic forms 101
10. 7 Root systems and root lattices 153
11. 8 Comparison of lattice classifications 171
12. 9 Applications 189
13. A. Basic notions of group theory with illustrative examples 211
14. B. Graphs, posets, and topological invariants 223
15. C. Notations for point and crystallographic groups 229
16. D. Orbit spaces for plane crystallographic groups 235
17. E. Orbit spaces for 3D-irreducible Bravais groups 243
18. Bibliography 251
19. Index 259