GeNoCAS 2026: Aidan Sims

Morita equivalence of graded C*-algebras. The Elliott classification programme aims to classify nuclear C*-algebras by means of K-theoretic invariants, although information beyond ordinary ordered K-theory is often required. In this talk, we will introduce the total K-theory together with the Bockstein operations, which include the coefficient maps ρ and κ, and the Bockstein maps β . We will show that the Bockstein operations are necessary for the classification of AD algebras with real rank zero. In fact, Eilers established that, for such algebras with bounded torsion in K_1 , the κ-maps are redundant in classification by the ordered scaled total K-theory. In this talk, we will address the unbounded torsion case and show a sharp contrast: the map κ is in fact essential. This is based on joint work with Zhichao Liu and Xin Ma.