Finite closed coverings of compact quantum spaces

• Autorzy: Piotr M. Hajac , Atabey Kaygun , Bartosz Zieliński
• Języki publikacji: EN

Abstrakty

EN

We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space $ℙ^∞$ the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported flabby sheaves of algebras is equivalent to the category of algebras with a finite set of ideals that intersect to zero and generate a distributive lattice. In particular, the Gelfand transform allows us to view finite closed coverings of compact Hausdorff spaces as flabby sheaves of commutative unital C*-algebras over $ℙ^∞$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2012
• Tom: 98
• Numer: 1
• Strony: 215-237

Daty

wydano

2012

Twórcy

autor

Piotr M. Hajac

• Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956 Warszawa, Poland
• Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski, Hoża 74, 00-682 Warszawa, Poland

autor

Atabey Kaygun

• Department of Mathematics and Computer Science, Bahçeşehir University, Çırağan Cad., Beşiktaş 34353 Istanbul, Turkey

autor

Bartosz Zieliński

• Department of Theoretical Physics and Computer Science, University of Łódź, Pomorska 149/153, 90-236 Łódź, Poland
• Mathematical Institute, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc98-0-8