Cargando…

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

Annotation

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:
Acceso en línea:Texto completo

MARC

LEADER 00000cam a2200000 i 4500
001 EBOOKCENTRAL_on1004831978
003 OCoLC
005 20240329122006.0
006 m o d
007 cr |n|||||||||
008 170928s2015 fr a gob 001 0 fre d
040 |a YDX  |b eng  |e pn  |c YDX  |d EBLCP  |d IDB  |d N$T  |d OCLCQ  |d EZ9  |d OCLCO  |d OCLCF  |d OCLCQ  |d OCLCO  |d CUY  |d LOA  |d ZCU  |d MERUC  |d ICG  |d COCUF  |d DKC  |d UX1  |d UKKNU  |d OCLCQ  |d GZL  |d UKAHL  |d ERD  |d OCLCO  |d OCLCQ  |d OCLCO  |d OCLCQ  |d OCLCO  |d OCLCL 
020 |a 9782759819522  |q (electronic bk.) 
020 |a 2759819523  |q (electronic bk.) 
020 |a 9782759817382  |q (electronic bk.) 
020 |a 2759817385  |q (electronic bk.) 
035 |a (OCoLC)1004831978 
037 |a 102204  |b Knowledge Unlatched 
050 4 |a QA171.5  |b .Z455 2015eb 
072 7 |a MAT  |x 000000  |2 bisacsh 
072 7 |a PHM  |2 bicssc 
082 0 4 |a 511.33  |2 23 
049 |a UAMI 
100 1 |a Zhilinskiĭ, B. I.  |q (Boris Igorevich)  |1 https://id.oclc.org/worldcat/entity/E39PCjDpH4yrM9H3MxBtktxcvb 
245 1 0 |a Introduction to Louis Michel's lattice geometry through group action /  |c Boris Zhilinskii, Michel Leduc, Michel Le Bellac. 
264 1 |a Les Ulis :  |b EDP sciences,  |c 2015. 
264 4 |c ©2015 
300 |a 1 online resource 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 0 |a Current Natural Sciences 
505 0 |a 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. 
505 8 |a 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. 
505 8 |a 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. 
505 8 |a 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. 
505 8 |a E -- Orbit spaces for 3D-irreducible Bravais groupsBibliography; Index. 
504 |a Includes bibliographical references and index. 
520 8 |a Annotation  |b Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the main 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 authors turn to different symmetry and topological classifications including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoi 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 done through a number of concrete examples with an extensive use of graphical visualization. The book is addressed to graduated and post-graduate students and young researches in theoretical physics, dynamical systems, applied mathematics, solid state physics, crystallography, molecular physics, theoretical chemistry ..." 
542 1 |f This work is licensed under a Creative Commons license  |u https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Lattice theory. 
650 6 |a Théorie des treillis. 
650 7 |a Atomic & molecular physics.  |2 bicssc 
650 7 |a MATHEMATICS  |x General.  |2 bisacsh 
650 7 |a Lattice theory  |2 fast 
700 1 |a Leduc, Michel. 
700 1 |a Le Bellac, Michel. 
758 |i has work:  |a Introduction to Louis Michel's lattice geometry through group action (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCFGKfcWgFrv6rrqt9twqYq  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |z 9782759817382  |z 2759817385  |w (OCoLC)936210752 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5057994  |z Texto completo 
936 |a BATCHLOAD 
938 |a Askews and Holts Library Services  |b ASKH  |n AH37555931 
938 |a EBL - Ebook Library  |b EBLB  |n EBL5057994 
938 |a EBSCOhost  |b EBSC  |n 1605172 
938 |a YBP Library Services  |b YANK  |n 14818064 
994 |a 92  |b IZTAP