Universal UHF algebra

Question

I am reading on quasidiagonal $C^*$-algebras. There the phrase "the universal UHF algebra" appears. I know what UHF algebras are, but I don't know what the universal UHF algebra is. I would be glad about an explanation or reference.

Answer 1

By the universal UHF algebra people usually mean the UHF algebra with the associated supernatural number: $$\prod_{p\in \mathbb{P}}p^\infty.$$ In other words, UHF algebra is the the unique UHF algebra $A$ with $K_0(A)=\mathbb{Q}$.

A good reference is Rørdam's Classification of Nuclear C${}^\ast$-Algebras.