2022/11/03 by Boava, Giuliano, de Castro, Gilles G., Gonçalves, Daniel +1
#06E15 #16S35 #16S88 #22A22 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Primary: 16S10. Secondary: 37B10 #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2211.02148
We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital and the other not necessarily. We focus on the unital case and describe a conjugacy between Ott-Tomforde-Willis subshifts in terms of a homeomorphism between the Stone duals of suitable Boolean algebras, and in terms of a diagonal-preserving isomorphism of the associated unital algebras. For this, we realise the unital algebra associated with a subshift as a groupoid algebra and as a partial skew group ring.