Applications of the theory of orders to crystallographic groups

1981 ◽  
pp. 37-92
Author(s):  
Wilhelm Plesken
Keyword(s):  
Crystallographic Groups

scholarly journals Crystallographic groups and flat manifolds from surface braid groups

2020 ◽  
pp. 107560
Author(s):  
Daciberg Lima Gonçalves ◽  
John Guaschi ◽  
Oscar Ocampo ◽  
Carolina de Miranda e Pereiro
Keyword(s):  
Braid Groups ◽  
Crystallographic Groups ◽  
Flat Manifolds

scholarly journals Complex crystallographic groups I

1982 ◽  
Vol 34 (4) ◽  
pp. 581-593 ◽  
Author(s):  
Syoshi TOKUNAGA ◽  
Masaaki YOSHIDA
Keyword(s):  
Crystallographic Groups

Elements of Group Theory The Classical Crystallographic Groups

1974 ◽  
pp. 235-262
Author(s):  
A. V. Shubnikov ◽  
V. A. Koptsik ◽  
David Harker
Keyword(s):  
Group Theory ◽  
Crystallographic Groups

Algebraic K-theory of Crystallographic Groups

2014 ◽  
Author(s):  
Daniel Scott Farley ◽  
Ivonne Johanna Ortiz
Keyword(s):  
Crystallographic Groups ◽  
K Theory

scholarly journals Double crystallographic groups and their representations on the Bilbao Crystallographic Server

2017 ◽  
Vol 50 (5) ◽  
pp. 1457-1477 ◽  
Author(s):  
Luis Elcoro ◽  
Barry Bradlyn ◽  
Zhijun Wang ◽  
Maia G. Vergniory ◽  
Jennifer Cano ◽  
...  
Keyword(s):  
Irreducible Representations ◽  
Site Symmetry ◽  
Crystallographic Groups ◽  
Space Groups ◽  
Symmetry Approach ◽  
Wyckoff Position ◽  
Double Space ◽  
Elementary Band ◽  
Symmetry Relations ◽  
Symmetry Operations

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPGandREPRESENTATIONS DSG). The toolDCOMPRELprovides compatibility relations between the irreducible representations of double space groups at differentkvectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The programDSITESYMimplements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the programBANDREPcalculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results ofBANDREPhave been extensively applied in the description of and the search for topological insulators.

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