Reducibility of Covers of AFT shifts

TY - JOUR

T1 - Reducibility of Covers of AFT shifts

AU - Bates, Teresa

AU - Eilers, Søren

AU - Pask, David

N1 - Keywords: math.DS; math.OA; 37B10, 46L05

PY - 2011/10

Y1 - 2011/10

N2 - In this paper we show that the reducibility structure of several covers of sofic shifts is a flow invariant. In addition, we prove that for an irreducible subshift of almost finite type the left Krieger cover and the past set cover are reducible. We provide an example which shows that there are non almost finite type shifts which have reducible left Krieger covers. As an application we show that the Matsumoto algebra of an irreducible, strictly sofic shift of almost finite type is not simple.

AB - In this paper we show that the reducibility structure of several covers of sofic shifts is a flow invariant. In addition, we prove that for an irreducible subshift of almost finite type the left Krieger cover and the past set cover are reducible. We provide an example which shows that there are non almost finite type shifts which have reducible left Krieger covers. As an application we show that the Matsumoto algebra of an irreducible, strictly sofic shift of almost finite type is not simple.

U2 - 10.1007/s11856-011-0107-4

DO - 10.1007/s11856-011-0107-4

M3 - Journal article

SN - 0021-2172

VL - 185

SP - 207

EP - 234

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -