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Gelfand duality for compact pospaces
De Rudder, Laurent
2017Topology, Algebra and Categories in Logic 2017


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Keywords :
l-algebra; Gelfand-Neumark-Stone duality; compact pospace; semi-ring; bounded archimedean semi algebra
Abstract :
[en] It is well known that the category of compact Hausdorff spaces is dually equivalent to the category of commutative C^\star-algebras. More generally, this duality can be seen as a part of a square of dualities between compact Hausdorff spaces, C^\star-algebras, compact regular frames and de Vries algebras. Three of these dualities have been extended to dualities between compact pospaces, stably compact frames and proximity frames, the fourth part of the square being lacking. We propose the category of bounded Archimedean l-semi-algebra to complete what will be the outside square of dualities and to extend to category of C^\star-algebras.
Disciplines :
Author, co-author :
De Rudder, Laurent ;  Université de Liège > Département de mathématique > Algèbre et logique
Language :
Title :
Gelfand duality for compact pospaces
Publication date :
June 2017
Event name :
Topology, Algebra and Categories in Logic 2017
Event place :
Prague, Czechia
Event date :
du 26 au 30 juin 2017
Audience :
Available on ORBi :
since 29 May 2017


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