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      JOINS AND COVERS IN INVERSE SEMIGROUPS AND TIGHT -ALGEBRAS

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      Bulletin of the Australian Mathematical Society
      Cambridge University Press (CUP)

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          Abstract

          We show Exel’s tight representation of an inverse semigroup can be described in terms of joins and covers in the natural partial order. Using this, we show that the ${C}^{\ast } $ -algebra of a finitely aligned category of paths, developed by Spielberg, is the tight ${C}^{\ast } $ -algebra of a natural inverse semigroup. This includes as a special case finitely aligned higher-rank graphs: that is, for such a higher-rank graph $\Lambda $ , the tight ${C}^{\ast } $ -algebra of the inverse semigroup associated to $\Lambda $ is the same as the ${C}^{\ast } $ -algebra of $\Lambda $ .

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          Most cited references15

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          Inverse semigroups and combinatorial C*-algebras

          Ruy Exel* (2008)
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            Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach

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              Inverse Semigroups

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                Author and article information

                Journal
                Bulletin of the Australian Mathematical Society
                Bull. Aust. Math. Soc.
                Cambridge University Press (CUP)
                0004-9727
                1755-1633
                August 2014
                January 10 2014
                August 2014
                : 90
                : 1
                : 121-133
                Article
                10.1017/S0004972713001111
                543d5669-a7fa-437f-83ba-590036ce99cf
                © 2014

                https://www.cambridge.org/core/terms

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