与Pisot单位有关的算术群及其符号动力学表示
An arithmetic group associated with a Pisot unit and its symbolic-dynamical representatiom
摘要：
对于一个给定的Pisot单位$β$，我们关联一个有限阿贝尔群，其大小似乎等于$β$的判别式。我们称之为Pisot群，并在$β$满足关系$Fin(β)=\Bbb Z[β]\cap[0,1)$的情况下，在双边$β$-紧群中找到它的表示。作为一个动机的定义，我们表明，Pisot群是内核的一些重要的算术编码的toral自同构给出的同伴矩阵自然与$β$。
英文摘要：
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 $β$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
