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Proceedings of the London Mathematical Society 2005 91(1):184-214; doi:10.1112/S0024611505015285
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© London Mathematical Society

Equivariant Flow Equivalence for Shifts of Finite Type, by Matrix Equivalence Over Group Rings

Mike Boyle and Michael C. Sullivan

Department of Mathematics, University of Maryland College Park, MD 20742-4015, USA. E-mail: mmb{at}math.umd.edu www.math.umd.edu/~mmb
Department of Mathematics, Southern Illinois University Carbondale, IL 62901-4408, USA. E-mail: msulliva{at}math.siu.edu www.math.siu.edu/sullivan

Received 10 June 2004. Revision received 10 December 2004.

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 K1(ZG). 2000 Mathematics Subject Classification 37B10 (primary), 15A21, 15A23, 15A33, 15A48, 19B28, 19M05, 20C05, 37D20, 37C80 (secondary).

Key Words: flow equivalence • shift of finite type • skew product • equivariant • K-theory • matrix equivalence • group ring • Smale flows • Markov


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