LEADER 03895 am 22005293u 450 001 996411338103316 005 20200520144314.0 010 $a2-7598-1952-3 024 7 $a10.1051/978-2-7598-1952-2 035 $a(CKB)3710000000738421 035 $a(Au-PeEL)EBL5057994 035 $a(CaPaEBR)ebr11445838 035 $a(OCoLC)1004831978 035 $a(DE-B1597)573347 035 $a(DE-B1597)9782759819522 035 $a(ScCtBLL)5bfeb78a-070f-4acd-bcb0-8814a5829ead 035 $a(MiAaPQ)EBC5057994 035 $a(PPN)203366530 035 $a(EXLCZ)993710000000738421 100 $a20171020h20152015 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aIntroduction to Louis Michel's lattice geometry through group action /$fB. Zhilinskii 210 1$aParis, [France] :$cEDP Sciences,$d2015. 210 4$d©2015 215 $a1 online resource (271 pages) $cillustrations 225 0 $aCurrent Natural Sciences 311 $a2-7598-1738-5 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tPreface -- $t1 Introduction -- $t2 Group action. Basic definitions and examples -- $t3 Delone sets and periodic lattices -- $t4 Lattice symmetry -- $t5 Lattices and their Voronoļ and Delone cells -- $t6 Lattices and positive quadratic forms -- $t7 Root systems and root lattices -- $t8 Comparison of lattice classifications -- $t9 Applications -- $tA. Basic notions of group theory with illustrative examples -- $tB. Graphs, posets, and topological invariants -- $tC. Notations for point and crystallographic groups -- $tD. Orbit spaces for plane crystallographic groups -- $tE. Orbit spaces for 3D-irreducible Bravais groups -- $tBibliography -- $tIndex 330 $aGroup 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. Voronoļ 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, . 606 $aLattice theory 615 0$aLattice theory. 676 $a511.33 700 $aZhilinskii?$b B.$0944459 702 $aLe Bellac$b Michel, $4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLeduc$b Michel, $4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996411338103316 996 $aIntroduction to Louis Michel's lattice geometry through group action$92131997 997 $aUNISA