Classification of real rank zero C*-algebras with finitely many ideals

With the classification theory of simple and nuclear C*-algebras of real rank zero advanced to a level which may very well be final, it is natural to wonder what happens when one allows ideals, but not too many of them. Contrasting the simple case, the K-theoretical classification theory for real rank zero C*-algebras with finitely many ideals is only satisfactorily developed in subcases, and in many settings it is even unclear and/or disputed which flavor of K-theory to use.

Restricting throughout to the setting of real rank zero, Søren Eilers will compare what is known of the classification of graph C*-algebras and of approximately subhomogeneous C*-algebras, with an emphasis on what kind of conclusion can be extracted from restrictions on the complexity of the ideal lattice. The results presented are either more than a decade old or joint with An, Liu and Gong.