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Type Theory of Special Classes of Boolean Inverse Semigroups

  • Friedrich Wehrung
Chapter
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Part of the Lecture Notes in Mathematics book series (LNM, volume 2188)

Abstract

While Theorem 4.8.9 implies that the type monoid of a Boolean inverse semigroup S can be any countable conical refinement monoid, there are situations in which the structure of S impacts greatly the one of \(\mathop{\mathrm{Typ}}\nolimits S\). A basic illustration of this is given by the class of AF inverse semigroups , introduced in Lawson and Scott [77], which is the Boolean inverse semigroup version of the class of AF C*-algebras. Another Boolean inverse semigroup version of a class of C*-algebras, which we will not consider here, is given by the Cuntz inverse monoids studied in Lawson and Scott [77, § 3].

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© Springer International Publishing AG 2017

Authors and Affiliations

  • Friedrich Wehrung
    • 1
  1. 1.Département de MathématiquesUniversité de Caen NormandieCaenFrance

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