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Equivariant Flow Equivalence for Shifts of Finite Type, by Matrix Equivalence Over Group Rings
Author(s) -
Boyle Mike,
Sullivan Michael C.
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611505015285
Subject(s) - mathematics , equivariant map , equivalence (formal languages) , pure mathematics , matrix equivalence , matrix group , algebra over a field , matrix analysis , symmetric group , physics , eigenvalues and eigenvectors , quantum mechanics
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).