A note on effect algebras and dimension theory of AF C\(^*\)-algebras
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.
scientific article; zbMATH DE number 5526751
scientific article