An arithmetic group associated with a Pisot unit and its symbolic-dynamical representatiom

Details An arithmetic group associated with a Pisot unit and its symbolic-dynamical representatiom An arithmetic group associated with a Pisot unit and its symbolic-dynamical representatiom

1999-12-23

arxiv.org/abs/math/9912194v1

Mathematics

Number Theory

10 pages in AMS-TeX

Scientific paper

To a given Pisot unit $\beta$ we associate a finite abelian group whose size appears to be equal to the discriminant of $\beta$. We call it the Pisot group and find its representation in the two-sided $\beta$-compactum in the case of $\beta$ satisfying the relation $Fin(\beta)=\Bbb Z[\beta]\cap[0,1)$. 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 $\beta$.

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