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SUMMARY:Ganna Kudryavtseva (University of Ljubjana)
DTSTART:20201028T113000Z
DTEND:20201028T123000Z
DTSTAMP:20260423T011112Z
UID:YSseminar/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/YSseminar/8/
 ">Boolean inverse semigroups</a>\nby Ganna Kudryavtseva (University of Lju
 bjana) as part of York semigroup seminar\n\n\nAbstract\nBoolean inverse se
 migroups are inverse semigroups whose idempotents admit a structure of a B
 oolean algebra and possessing joins of compatible pairs of elements. Non-c
 ommutative Stone duality connects Boolean inverse semigroups with Stone gr
 oupoids which are \\'etale topological groupoids whose space of identities
  is a Stone space. The focus of the talk will be on the speaker's recent w
 ork on $X$-to-join representations of inverse semigroups in Boolean invers
 e semigroups which are a relaxation of the notion of a cover-to-join repre
 sentation. We construct the universal $X$-to-join  Booleanization of an in
 verse semigroup $S$ as a weakly meet-preserving quotient of the universal 
  Booleanization ${\\mathrm B}(S)$ and show that all such quotients of ${\\
 mathrm B}(S)$ arise via $X$-to-join representaions.  As an application\, w
 e provide groupoid models for the intermediate boundary quotients of the $
 C^*$-algebra of a Zappa-Szép product right LCM semigroup by  Brownlowe\, 
 Ramagge\, Robertson and Whittaker.\n
LOCATION:https://researchseminars.org/talk/YSseminar/8/
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