作为$\mathbb{T}^{n}$自同构共轭不变量的Bowen-Franks群
Bowen-Franks groups as conjugacy invariants for $\mathbb{T}^{n}$ automorphisms
摘要：
研究了广义Bowen-Franks群（BF-群）作为$\mathbb{T}^{n}$自同构的拓扑共轭不变量的作用.利用代数数论，建立了不同自同构的BF-群的相等性（$BF$ -等价）和有限格中的同一位置（$\mathcal{L}$ -等价）之间的联系.证明了这两个条件等价的重要情况。最后，给出了经典BF群$\mathbb{Z}% ^{n}/\mathbb{Z}^{n}(I-A)$的拓扑解释.
英文摘要：
The role of generalized Bowen-Franks groups (BF-groups) as topological conjugacy invariants for $\mathbb{T}^{n}$ automorphisms is studied. Using algebraic number theory, a link is established between equality of BF-groups for different automorphisms ($BF$-equivalence) and an identical position in a finite lattice ($\mathcal{L}$-equivalence). Important cases of equivalence of the two conditions are proved. Finally, a topological interpretation of the classical BF-group $\mathbb{Z}% ^{n}/\mathbb{Z}^{n}(I-A)$ in this context is presented.
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