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作者 Zhilinskii, B
書名 Introduction to Louis Michel's Lattice Geometry Through Group Action
出版項 Les Ulis : EDP Sciences, 2015
©2017
國際標準書號 9782759819522 (electronic bk.)
9782759817382
book jacket
說明 1 online resource (271 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Current Natural Sciences Ser
Current Natural Sciences Ser
附註 Intro -- 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 lattices -- 5 - 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 parallelohedra -- 6.7 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 tiling
9.2 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 groups -- Bibliography -- Index
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Zhilinskii, B. Introduction to Louis Michel's Lattice Geometry Through Group Action Les Ulis : EDP Sciences,c2015 9782759817382
主題 Lattice theory
Electronic books
Alt Author Leduc, Michel
Le Bellac, Michel
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