The Atiyah conjecture for the Hecke algebra of the infinite dihedral group

TL;DR

This paper proves a generalized Strong Atiyah Conjecture for the infinite dihedral group by replacing the group von Neumann algebra with the Hecke-von Neumann algebra, extending previous results in operator algebras.

Contribution

It introduces a generalized version of the Strong Atiyah Conjecture for the infinite dihedral group using Hecke-von Neumann algebras, expanding the scope of the conjecture.

Findings

Proved the generalized Strong Atiyah Conjecture for the infinite dihedral group.

Replaced the group von Neumann algebra with the Hecke-von Neumann algebra in the conjecture.

Extended the applicability of the Atiyah conjecture to Hecke algebra settings.

Abstract

We prove a generalized version of the Strong Atiyah Conjecture for the infinite dihedral group W, replacing the group von Neumann algebra NW with the Hecke-von Neumann algebra N_qW.