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

Nikita Sidorov
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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 $Fin(β)=\Bbb Z[β]\cap[0,1)$. 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 $β$.

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Nikita Sidorov. 1999-12-23. An arithmetic group associated with a Pisot unit and its symbolic-dynamical representatiom. https://arxiv.org/abs/math/9912194

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