The universal Boolean inverse semigroup presented by the abstract\n Cuntz-Krieger relations

2019/02/07 by Mark V. Lawson, Lawson, Mark V, Alina Vdovina +1 · 2 citations
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Operator Algebras (math.OA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1902.02583

openalex publication_date 2019/02/07 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

This paper is a contribution to the theory of what might be termed\n0-dimensional non-commutative spaces. We prove that associated with each\ninverse semigroup S is a Boolean inverse semigroup presented by the abstract\nversions of the Cuntz-Krieger relations. We call this Boolean inverse semigroup\nthe Exel completion of S and show that it arises from Exel's tight groupoid\nunder non-commutative Stone duality.\n

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