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oapen-20.500.12657-250122021-11-09T09:29:49Z Introduction to Louis Michel's lattice geometry through group action Zhilinskii, Boris Mathematics cristallography group theory bic Book Industry Communication::P Mathematics & science::PH Physics::PHM Atomic & molecular physics 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. 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. 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 appl 2019-10-23 03:00:36 2020-04-01T10:17:49Z 2020-04-01T10:17:49Z 2016-03-03 book 1005090 OCN: 1135854835 9782759819522 http://library.oapen.org/handle/20.500.12657/25012 eng application/pdf n/a 1005090.pdf http://laboutique.edpsciences.fr/produit/833/9782759819522/Introduction%20to%20Louis%20Michels%20lattice%20geometry%20through%20group%20action?search_ EDP SCIENCES 102204 72a84c7e-1385-4e97-8aa9-11c618327100 b818ba9d-2dd9-4fd7-a364-7f305aef7ee9 9782759819522 Knowledge Unlatched (KU) 102204 KU Select 2018: STEM Backlist Books Knowledge Unlatched open access
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OAPEN
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English
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| description |
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. 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.
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 appl
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1005090.pdf
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1005090.pdf
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1005090.pdf
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1005090.pdf
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1005090.pdf
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1005090.pdf
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1005090.pdf
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EDP SCIENCES
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2019
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http://laboutique.edpsciences.fr/produit/833/9782759819522/Introduction%20to%20Louis%20Michels%20lattice%20geometry%20through%20group%20action?search_
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