Introduction to Louis Michel's lattice geometry through group action
Author(s)
Zhilinskii, Boris
Collection
Knowledge Unlatched (KU)Number
102204Language
EnglishAbstract
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 appl
Keywords
Mathematics; cristallography; group theory; TextbookISBN
9782759819522OCN
1135854835Publisher
EDP SCIENCESPublisher website
https://www.edpsciences.org/fr/Publication date and place
2016-03-03Classification
Atomic and molecular physics