10 Even unimodular lattices in small dimensions

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An Introduction to Groups and Lattices：作者：Robert L. Griess,Jr　　 ISBN：978-7-04-029205-3　出版时间：2010-06-07

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目录

1 Introduction

2 Bilinear Forms, Quadratic Forms and Their Isometry Groups

3 General Results on Finite Groups and Invariant Lattices

4 Root Lattices of Types A, D, E

5 Hermite and Minkowski Functions

6 Constructions of Lattices by Use of Codes

7 Group Theory and Representations

8 Overview of the Barnes-Wall Lattices

9 Construction and Properties of the Barnes-Wall Lattices

10 Even unimodular lattices in small dimensions

11 Pieces of Eight

References

Index

Appendix A The Finite Simple Groups

Appendix B Reprints of Selected Articles

ADVANCED LECTURES IN MATHEMATICS
- 10.1 Classifications of even unimodular lattices
- 10.2 Constructions of some Niemeier lattices
- 10.2.1 Construction of a Leech lattice
- 10.3 Basic theory of the Golay code
- 10.3.1 Characterization of certain Reed-Muller codes
- 10.3.2 About the Golay code
- 10.3.3 The octad Triangle and dodecads
- 10.3.4 A uniqueness theorem for the Golay code
- 10.4 Minimal vectors in the Leech lattice
- 10.5 First proof of uniqueness of the Leech lattice
- 10.6 Initial results about the Leech lattice
- 10.6.1 An automorphism which moves the standard frame
- 10.7 Turyn-style construction of a Leech lattice
- 10.8 Equivariant unimodularizations of even lattices

10 Even unimodular lattices in small dimensions

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