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Introduction to Louis Michel's lattice geometry through group action
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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
This book is made open access as part of the Knowledge Unlatched KU Select 2018: STEM Backlist Books
This book is made open access as part of the Knowledge Unlatched KU Select 2018: STEM Backlist Books
This book is included in DOAB.
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- cristallography
- Group theory
- KUnlatched
- Mathematics
- MATHEMATICS / Discrete Mathematics
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