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Chapter 6 is a short outlook on feasible and necessary follow-up comparative research projects towards solid reconstructions of the other branches of Chadic besides Central Chadic, not least in order to arrive at a robust reconstruction of Proto-Chadic as a whole. Further, the list of petrified morphological markers provides a starting point for reconstructing their original functions based on a comparative analysis of their synchronic functions in the modern Chadic languages. We would also want a fairly complete collection of isogloss maps for words and linguistic features for Central Chadic and later also for the other branches of the Chadic language family.

We apply a method inspired by Popa's intertwining-by-bimodules technique to investigate inner conjugacy of MASAs in graph $C^*$-algebras. First, we give a new proof of non-inner conjugacy of the diagonal MASA ${\mathcal {D}}_E$ to its non-trivial image under a quasi-free automorphism, where $E$ is a finite transitive graph. Changing graphs representing the algebras, this result applies to some non quasi-free automorphisms as well. Then, we exhibit a large class of MASAs in the Cuntz algebra ${\mathcal {O}}_n$ that are not inner conjugate to the diagonal ${\mathcal {D}}_n$.

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6 - Outlook

Summary

On conjugacy of subalgebras in graph C*-algebras. II

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6 - Outlook

Summary

On conjugacy of subalgebras in graph C*-algebras. II