Mac Lane method in the investigation of magnetic translation groups

Details Mac Lane method in the investigation of magnetic translation groups Mac Lane method in the investigation of magnetic translation groups

1998-03-14

arxiv.org/abs/cond-mat/9803186v1

Rep. Math. Phys. 38 (1996) 325-332

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages, 1 fig. in text, romp_sty.tex attached at the beginning Presented at 28 Symp. on Math. Phys., Torun 2-6 Dec 1995

Scientific paper

Central extensions of the three-dimensional translation group T=Z^3 by the unitary group U(1) (a group of factors) are considered within the frame of the Mac~Lane method. All nonzero vectors t in T are considered to be generators of T. This choice leads to very illustrative relations between the Mac~Lane method and Zak's approach to magnetic translation groups. It is shown that factor systems introduced by Zak and Brown can be realized only for the unitary group U(1) and for some of its finite subgroups.

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