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arXiv · 2103.02962

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

Sven Raum·Adam Skalski
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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.

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Sven Raum, Adam Skalski. 2021-03-04. Classifying right-angled Hecke C*-algebras via K-theoretic invariants. https://arxiv.org/abs/2103.02962

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