Classifying right-angled Hecke C*-algebras via K-theoretic invariants

Abstract

Exploiting the graph product structure and results concerning amalgamated free products of C⁎-algebras we provide an explicit computation of the K-theoretic invariants of right-angled Hecke C⁎-algebras, including concrete algebraic representants of a basis in K-theory. On the way, we show that these Hecke algebras are KK-equivalent with their undeformed counterparts and satisfy the UCT. Our results are applied to study the isomorphism problem for Hecke C⁎-algebras, highlighting the limits of K-theoretic classification, both for varying Coxeter type as well as for fixed Coxeter type.