Hostname: page-component-7bb8b95d7b-lvwk9 Total loading time: 0 Render date: 2024-09-12T12:17:15.838Z Has data issue: false hasContentIssue false
  • English
  • Français

Equivariant flow equivalence for shifts of finite type, by matrix equivalence over group rings

Published online by Cambridge University Press:  22 June 2005

Mike Boyle  and
Michael C. Sullivan
Mike Boyle
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA. E-mail: mmb@math.umd.eduwww.math.umd.edu/~mmb
Michael C. Sullivan
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, USA. E-mail: msulliva@math.siu.edu, www.math.siu.edu/sullivan
Get access

Abstract

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 $K_1(ZG)$.

Keywords

flow equivalenceshift of finite typeskew productequivariantK-theorymatrix equivalencegroup ringSmale flowsMarkov37B10 (primary)15A2115A2315A3315A4819B2819M0520C0537D2037C80 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 91 , Issue 1 , July 2005 , pp. 184 - 214
Copyright
2005 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)