An arithmetic group associated with a Pisot unit and its symbolic-dynamical representatiom
Abstract
To a given Pisot unit β we associate a finite abelian group whose size appears to be equal to the discriminant of β. We call it the Pisot group and find its representation in the two-sided β-compactum in the case of β satisfying the relation Fin(β)= Z[β][0,1). As a motivation for the definition, we show that the Pisot group is the kernel of some important arithmetic coding of the toral automorphism given by the companion matrix naturally associated with β.
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