Introduction to Louis Michel's lattice geometry through group action /

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Zhilinskiĭ, B. I. (Boris Igorevich)
Otros Autores: Leduc, Michel, Le Bellac, Michel
Formato: Electrónico eBook
Idioma:Francés
Publicado: Les Ulis : EDP sciences, 2015.
Colección:Current Natural Sciences
Temas:
Lattice theory.
Théorie des treillis.
Atomic & molecular physics.
MATHEMATICS > General.
Lattice theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction to Louis Michel's lattice geometry through group action; Contents; Preface; 1
  • Introduction; 2
  • Group action. Basic definitions and examples; 2.1 The action of a group on itself; 2.2 Group action on vector space; 3
  • Delone sets and periodic lattices; 3.1 Delone sets; 3.2 Lattices; 3.3 Sublattices of L; 3.4 Dual lattices; 4
  • Lattice symmetry; 4.1 Introduction; 4.2 Point symmetry of lattices; 4.3 Bravais classes; 4.4 Correspondence between Bravais classes and lattice point symmetry groups; 4.5 Symmetry, stratification, and fundamental domains.
  • 4.6 Point symmetry of higher dimensional lattices5
  • Lattices and their Voronoïand Delone cells; 5.1 Tilings by polytopes: some basic concepts; 5.2 Voronoï cells and Delone polytopes; 5.3 Duality; 5.4 Voronoï and Delone cells of point lattices; 5.5 Classification of corona vectors; 6
  • Lattices and positive quadratic forms; 6.1 Introduction; 6.2 Two dimensional quadratic forms and lattices; 6.3 Three dimensional quadratic forms and 3D-lattices; 6.4 Parallelohedra and cells for N-dimensional lattices; 6.5 Partition of the cone of positive-definite quadratic forms.
  • 6.6 Zonotopes and zonohedral families of parallelohedra6.7 Graphical visualization of members of the zonohedral family; 6.8 Graphical visualization of non-zonohedral lattices; 6.9 On Voronoï conjecture; 7
  • Root systems and root lattices; 7.1 Root systems of lattices and root lattices; 7.2 Lattices of the root systems; 7.3 Low dimensional root lattices; 8
  • Comparison of lattice classifications; 8.1 Geometric and arithmetic classes; 8.2 Crystallographic classes; 8.3 Enantiomorphism; 8.4 Time reversal invariance; 8.5 Combining combinatorial and symmetry classification; 9
  • Applications.
  • 9.1 Sphere packing, covering, and tiling9.2 Regular phases of matter; 9.3 Quasicrystals; 9.4 Lattice defects; 9.5 Lattices in phase space. Dynamical models. Defects; 9.6 Modular group; 9.7 Lattices and Morse theory; A
  • Basic notions of group theory with illustrative examples; B
  • Graphs, posets, and topological invariants; C
  • Notations for point and crystallographic groups; C.1 Two-dimensional point groups; C.2 Crystallographic plane and space groups; C.3 Notation for four-dimensional parallelohedra; D
  • Orbit spaces for planecrystallographic groups.
  • E
  • Orbit spaces for 3D-irreducible Bravais groupsBibliography; Index.

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