Applications of model theory to \(C^*\)-dynamics (Q1653297)

This paper deals with compact group actions on \(C^*\)-algebras from a model-theoretic viewpoint. It is proved that the continuous part of the central sequence algebra of a strongly self-absorbing action is indistinguishable from the continuous part of the sequence algebra, and in fact is equivariantly isomorphic under the continuum hypothesis. A unified approach is given to several dimensional inequalities in \(C^*\)-algebra theory. It is proved that whenever a \(C^*\)-algebra \(A\) absorbs a strongly self-absorbing \(C^*\)-algebra \(D\), and \(\alpha\) is an action of a compact group \(G\) on \(A\) with finite Rokhlin dimension with commuting towers, then \(\alpha\) absorbs any strongly self-absorbing action of \(G\) on \(D\). In many cases of interest, the results of this paper restrict the possible values of the Rokhlin dimension to \(0\), \(1\) and \(\infty\). Finally, it is shown that an action of a finite group with finite Rokhlin dimension with commuting towers automatically has the Rokhlin property if the algebra is UHF-absorbing.