Magnetic translation groups as group extension

Physics – Condensed Matter – Mesoscale and Nanoscale Physics

Scientific paper

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10 pages

Scientific paper

Extensions of a direct product T of two cyclic groups Z_n1 and Z_n2 by an
Abelian (gauge) group G with the trivial action of T on G are considered. All
possible (nonequivalent) factor systems are determined using the Mac Lane
method. Some of resulting groups describe magnetic translation groups. As
examples extensions with G=U(1) and G=Z_n are considered and discussed.

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