Abstract
The role of generalized Bowen–Franks groups (BF-groups) as topological conjugacy invariants for $$ \mathbb{T}^{n} $$ -automorphisms is studied, including a topological interpretation of the classical BF-group $$ \mathbb{Z}^{n} /\mathbb{Z}^{n} (I - A) $$ in this context. 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.
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