2017/10/12 by R. Exel, Exel, R., Benjamin Steinberg +1
Computer Science · Mathematics · #20M18 #46L55 #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1710.04722
openalex publication_date 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a semigroup S with zero, which is left-cancellative in the sense that st=sr ≠ 0 implies that t=r, we construct an inverse semigroup called the inverse hull of S, denoted H(S). When S admits least common multiples, in a precise sense defined below, we study the idempotent semilattice of H(S), with a focus on its spectrum. When S arises as the language semigroup for a subsift X on a finite alphabet, we discuss the relationship between H(S) and several C*-algebras associated to X appearing in the literature.