Subshifts and their algebras

Abstract

In these notes, we study subshifts, with an emphasis on subshifts over infinite alphabets and their associated noncommutative algebras. In particular, we introduce Ott–Tomforde–Willis (OTW) subshifts and show that while they share some properties with classical subshifts over finite alphabets, they also exhibit distinct behaviours. Our focus is on the study of conjugacy between subshifts and the description of invariants for conjugacy via the associated noncommutative algebras, both in the algebraic and analytic settings. In the algebraic setting, we employ the socle of the subshift algebra, whereas in the analytic setting, we use the K-theory of the associated C${}^{\ast }$-algebra.