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

TL;DR

This paper computes K-theoretic invariants for right-angled Hecke C*-algebras using graph product structures, demonstrating KK-equivalence with undeformed algebras and exploring classification limits.

Contribution

It provides explicit K-theoretic computations and shows KK-equivalence, advancing understanding of the classification of Hecke C*-algebras.

Findings

Explicit K-theoretic invariants computed

Hecke algebras are KK-equivalent to undeformed versions

Limits of K-theoretic classification discussed

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.