Divisibility properties for C*-algebras

Leonel Robert; Mikael Rørdam

doi:10.1112/plms/pds082

Divisibility properties for C*-algebras

Leonel Robert, Mikael Rørdam

Institut for Matematiske Fag

10 Citationer (Scopus)

Abstract

We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility behaviour. As a byproduct of our investigations, we show that there exists a sequence (An) of simple unital infinite dimensional C*-algebras such that the product ∏n=1∞ An has a character.

Originalsprog	Engelsk
Tidsskrift	Proceedings of the London Mathematical Society
Vol/bind	106
Udgave nummer	6
Sider (fra-til)	1330-1370
ISSN	0024-6115
DOI	https://doi.org/10.1112/plms/pds082
Status	Udgivet - jun. 2013

Adgang til dokumentet

10.1112/plms/pds082

Citationsformater

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abstract = "We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility behaviour. As a byproduct of our investigations, we show that there exists a sequence (An) of simple unital infinite dimensional C*-algebras such that the product ∏n=1∞ An has a character.",

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AU - Rørdam, Mikael

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AB - We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility behaviour. As a byproduct of our investigations, we show that there exists a sequence (An) of simple unital infinite dimensional C*-algebras such that the product ∏n=1∞ An has a character.

U2 - 10.1112/plms/pds082

DO - 10.1112/plms/pds082

M3 - Journal article

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VL - 106

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JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 6

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