Strongly outer product type actions

Abstract

We show that for any countable discrete maximally almost periodic group $G$ and any UHF algebra $A$, there exists a strongly outer product type action $\alpha$ of $G$ on $A$. We also show the existence of countable discrete almost abelian group actions with a certain Rokhlin property on the universal UHF algebra. Consequently we get many examples of unital separable simple nuclear $C^{\ast }$-algebras with tracial rank zero and a unique tracial state appearing as crossed products.

36 pages total. Exposition simplified: removed proofs of well-known operator algebra facts etc. Added section to emphasize the ideas of bumping up and cutting down used. Now 22 pages. Lengthy but routine proofs deferred to thesis, exposition simplified

References in corpus (2)

• Localizing the Elliott conjecture at strongly self-absorbing C*-algebras
• Existence of the Matui-Sato tracial Rokhlin property