Symmetries and reversing symmetries of toral automorphisms

Details Symmetries and reversing symmetries of toral automorphisms Symmetries and reversing symmetries of toral automorphisms

2000-06-13

arxiv.org/abs/math/0006092v1

Mathematics

Dynamical Systems

34 pages

Scientific paper

10.1088/0951-7715/14/4/201

Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their connection with unit groups in orders of algebraic number fields. For the question of reversibility, we derive necessary conditions in terms of the characteristic polynomial and the polynomial invariants. We also briefly discuss extensions to (reversing) symmetries within affine transformations, to PGL(n,Z) matrices, and to the more general setting of integer matrices beyond the unimodular ones.

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