Towards a system in space group representations
type: Item
instance of: scholarly article
title: Towards a system in space group representations
zbMATH Open document ID: 0663.20050
DOI: 10.1016/0898-1221(88)90240-4
publication date: 1988-01-01T00:00:00Z
review text: There are several manuals for deriving the irreducible representations of space groups, but that is not enough for getting a real insight view of the matter, which is far more rich than one would expect at first. The paper goes beyond the contents covered by the title and at the same time deals with a first approach, more than with a full treatment. It reflects the remarkable effort of the author to understand crystallographic groups through a hierarchical approach where higher dimensional (R- and Q-reducible) space groups are obtained from lower dimensional irreducible ones. Within this perspective, subperiodic groups (i.e. layer and rod group types) play a natural role. About the systematic in space group representation, the general idea is simple: one has to consider not only the normal subgroup, kernel of the homomorphism defining the irreducible representation, but the whole lattice of normal subgroups of a given spacegroup if one is looking for general properties, more than for special cases only. Again there is an important relation between this lattice and that of normal subgroups of corresponding layer and rod subgroups. As next step the author announces the investigation between the normal subgroup lattice and the irreducible representations themselves, together with what they imply (Clebsch-Gordan products in particular).
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 4083931
zbMATH Keywords: irreducible representations of space groups
zbMATH Keywords: crystallographic groups
zbMATH Keywords: subperiodic groups
zbMATH Keywords: lattice of normal subgroups
zbMATH Keywords: layer and rod subgroups
zbMATH Keywords: Clebsch-Gordan products
author: Vojtěch Kopský
reviewed by: A. Janner
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90240-4
OpenAlex ID: W2169506090
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4083931