Introduction to lattice geometry through group action

Édition en anglais

Boris Zhilinskií - Collection Savoirs actuels - Mathématiques

270 pages, parution le 04/12/2015

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Résumé

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. Different 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 different symmetry and topological classifications 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, ...

L'auteur - Boris Zhilinskií

Boris Zhilinskií est professeur à l'université du Littoral Côte d'Opale. Chimiste de formation, sa recherche porte sur l'analyse mathématique de systèmes atomiques ou moléculaires. Il a déjà publié trois livres en russe sur les spectres complexes de molécules et des articles de revue sur les applications de la symétrie.

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Caractéristiques techniques

	PAPIER	NUMERIQUE
Éditeur(s)	EDP Sciences
Auteur(s)	Boris Zhilinskií
Collection	Savoirs actuels - Mathématiques
Parution	04/12/2015	04/12/2015
Nb. de pages	270	271
Format	15.8 x 23.5	-
Couverture	Broché	-
Poids	528g	-
Contenu	-	PDF
EAN13	9782759817382	9782759819522