Divisibility properties for C*-algebras

Leonel Robert; Mikael Rørdam

doi:10.1112/plms/pds082

Divisibility properties for C*-algebras

Leonel Robert, Mikael Rørdam

Department of Mathematical Sciences

10 Citations (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.

Original language	English
Journal	Proceedings of the London Mathematical Society
Volume	106
Issue number	6
Pages (from-to)	1330-1370
ISSN	0024-6115
DOIs	https://doi.org/10.1112/plms/pds082
Publication status	Published - Jun 2013

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10.1112/plms/pds082

Cite this

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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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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.

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DO - 10.1112/plms/pds082

M3 - Journal article

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JF - Proceedings of the London Mathematical Society

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