Automorphisms and Discrete Fiber Bundles

Peter Kramer, Uwe Beck and Shelomo I. Ben-Abraham
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Peter Kramer: Universität Tübingen, Institut für Theoretische Physik
Uwe Beck: Universität Tübingen, Institut für Theoretische Physik
Shelomo I. Ben-Abraham: Ben-Gurion University of the Negev, Physics Department

A chapter in Symmetries in Science IX, 1997, pp 179-192 from Springer

Abstract: Abstract The motivation of the present work is twofold. In an attempt to generalize notions of crystallography for the description of systems with broken translational symmetry as for example quasicrystals, a scheme with non-commutative translations was explored [1, 2]. This scheme is strictly discrete. It is based on free groups and their automorphisms, and is linked to standard crystallography through two basic homomorphisms. In particular for the 17 space groups on the plane, 17 non-commutative preimages were constructed.

Keywords: Normal Subgroup; Fiber Bundle; Cayley Graph; Closed Path; Commutator Subgroup (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-1-4615-5921-4_13

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