Ganna Kudryavtseva: Prime representations of inverse semigroups

We discuss prime representations of  inverse semigroups in distributive inverse semigroups.

We start from the much easier but illuminating case of semilattices, where prime filters generalize the usual notion of a prime filter in a distributive lattice. This is parallel to the fact that

tight filters in a semilattice generalize ultrafilters of Boolean algebras. The construction of the prime groupoid of an inverse

semigroup is similar to the construction of the tight groupoid. We discuss prime representations of graph inverse semigroups

 and express the canonical representation as the "relative Booleanization" of graph inverse semigroups, which is similar to the notion of the relative graph C^* algebra.

 

Roman Drnovšek in Primož Moravec