Michael Baake and John A G Roberts 2001 Nonlinearity 14 R1 doi:10.1088/0951-7715/14/4/201
Symmetries and reversing symmetries of toral automorphisms
REVIEW ARTICLEMichael Baake1,3 and John A G Roberts2,4
Show affiliationsREVIEW ARTICLE
Recommended by J P Keating
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,
) matrices with a 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,) matrices, and to the more general setting of integer matrices beyond the unimodular ones.
- PACS
- MSC
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15A36 Matrices of integers (See also 11C20)
12D05 Polynomials: factorization
20G25 Linear algebraic groups over local fields and their integers
- Subjects
- Dates
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Issue 4 (July 2001)
Received 13 June 2000, in final form 23 February 2001
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Symmetries and reversing symmetries of toral automorphisms
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