ABSTRACT We establish a matrix characterization (called block conjugacy) of the notion of weak equivalence of ideals. This gives the existence of a one-to-one correspondence between equivalence classes of block conjugate toral automorphisms (of a given irreducible characteristic polynomial) and equivalence classes of the weakly equivalent associated ideals. We show that there exist nonconjugate irreducible hyperbolic toral automorphisms A and B for which and are conjugate.

中文翻译：

---

不可约托自同构的块共轭

摘要 我们建立了理想弱等价概念的矩阵表征（称为块共轭）。这给出了块共轭环自同构（给定不可约特征多项式）的等价类与弱等价相关理想的等价类之间存在一对一的对应关系。我们证明存在非共轭不可约双曲自同构 A 和 B，其中 和 是共轭的。