Abstract. 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 numbers: 02.10, 0210, 0220

Print publication: Issue 4 (July 2001)
Received 13 June 2000, in final form 23 February 2001