A decade ago, Katsoulis and Ramsey initiated a program that asked to what extent noncommutative algebraic dynamics can be recovered from noncommutative topological dynamics. More precisely, the problem asks to determine the smallest C*-algebra of the non-self-adjoint reduced and full crossed product operator algebras. For a broad class of examples, the problem was shown to be equivalent to understanding the gauge symmetries of the so-called Cuntz-Pimsner C*-algebras, which occupy a prominent role in noncommutative geometry. In joint work with Adam Dor-On, we gave a complete positive answer to the reduced case and now, we provide a corresponding negative answer for full crossed products.
