Mike Boyle and Michael C. Sullivan

Let $G$ be a finite group. We classify $G$-equivariant flow equivalence of non-trivial irreducible shifts of finite type in terms of

(i) elementary equivalence of matrices over $ZG$ and

(ii) the conjugacy class in $ZG$ of the group of G-weights of cycles based at a fixed vertex.

In the case $G = Z/2$, we have the classification for twistwise flow equivalence. We include some algebraic results and examples related to the determination of $E(ZG)$ equivalence, which involves $K_1(ZG)$.

2000 Mathematics Subject Classification: 37B10 (primary), 15A21, 15A23, 15A33, 15A48, 19B28, 19M05, 20C05, 37D20, 37C80 (secondary).

Keywords: flow equivalence, shift of finite type, skew product, equivariant, K-theory, matrix equivalence, group ring, Smale flows, Markov.

E-mail:
mmb@math.umd.edu
msulliva@math.siu.edu