A note on effect algebras and dimension theory of AF C\(^*\)-algebras
type: Item
instance of: scholarly article
title: A note on effect algebras and dimension theory of AF C\(^*\)-algebras
zbMATH Open document ID: 1165.81011
DOI: 10.1016/S0034-4877(08)80026-2
author: Anna Jenčová
author: Sylvia Pulmannová
published in: Reports on Mathematical Physics
publication date: 2009-03-09T00:00:00Z
review text: In [``Effect algebras with the Riesz decomposition property and AF C*-algebras'', Found. Phys. 29, No. 9, 1389--1402 (1999)], the second author initiated investigation of connections between effect algebras and approximately finite-dimensional (AF) C*-algebras. This investigation is now continued. Dimension effect algebras are defined, in analogy with dimension groups, as direct limits of finite effect algebras with Riesz Decomposition Property (RDP). Every dimension algebra is shown to be a unit interval in a dimension group with unit. The categories of countable dimension effect algebras and of unital AF C*-algebras are proved to be equivalent (this result was announced already in [loc. cit.]. Moreover, they both are equivalent to the category of countable dimension groups.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 20K99
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 5526751
zbMATH Keywords: C*-algebra
zbMATH Keywords: dimension group
zbMATH Keywords: effect algebra
zbMATH Keywords: \(K_0\)-group
zbMATH Keywords: Riesz decomposition property
MaRDI profile type: Publication
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full work available at URL: s0034-4877(08)80026-2
OpenAlex ID: W2040608653
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description: scientific article; zbMATH DE number 5526751