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

• Autores: Mike Boyle, Michael C. Sullivan
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 91, Nº 1, 2005, págs. 184-214
• Idioma: inglés
• DOI: 10.1112/s0024611505015285
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• Resumen

  • 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 $K_1(ZG)$.