Delocalised traces on Hecke algebras of right-angled, hyperbolic type

TL;DR

This paper constructs a smooth subalgebra for Hecke C*-algebras of right-angled, hyperbolic type, extending traces from conjugacy classes and demonstrating their faithfulness on K-theory.

Contribution

It introduces a new smooth subalgebra for these Hecke algebras and extends delocalised traces to this setting, analyzing their K-theoretic pairings.

Findings

Delocalised traces are extended to the smooth subalgebra.

The pairing of traces with K-theory is shown to be faithful.

Provides a new framework for analyzing traces on hyperbolic Coxeter-related algebras.

Abstract

For every Hecke C*-algebra of right-angled, hyperbolic type, we construct a smooth subalgebra to which traces associated with arbitrary conjugacy classes in the associated Coxeter group extend. We calculate the pairing with K-theory of the delocalised traces arising this way, showing that it is faithful on K-theory.