Introduction to Louis Michel's lattice geometry through group action

Boris Zhilinskii; Michel Leduc; Michel Le Bellac

book: Introduction to Louis Michel's lattice geometry through group action

Open Access Published by EDP Sciences 2016

Introduction to Louis Michel's lattice geometry through group action

Boris Zhilinskii , Michel Leduc and Michel Le Bellac

In the series Current Natural Sciences

https://doi.org/10.1051/978-2-7598-1952-2

Overview
Contents

About this book

Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Di erent basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to di erent symmetry and topological classi- cations including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoï and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach. Along with crystallographic applications, qualitative features of lattices of quantum states appearing for quantum problems associated with classical Hamiltonian integrable dynamical systems are shortly discussed. The presentation of the material is presented through a number of concrete examples with an extensive use of graphical visualization. The book is aimed at graduated and post-graduate students and young researchers in theoretical physics, dynamical systems, applied mathematics, solid state physics, crystallography, molecular physics, theoretical chemistry, ...

Topics

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

(Deutsch)

Language: English
Publisher: EDP Sciences
Audience: College/higher education;
Pages
- Main content: 262
Keywords: General Physics

eBook

Published: February 11, 2021
ISBN: 9782759819522

Hardcover

Published: December 4, 2015
ISBN: 9782759817382