C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type

TL;DR

This paper investigates the structure and K-theory of C*-algebras generated by specific monoids, providing new methods for computing K-theory in related group C*-algebras and crossed products.

Contribution

It offers novel structural insights into C*-algebras from right LCM one-relator and Artin-Tits monoids, including a new approach to K-theory calculations.

Findings

Established nuclearity, ideal structure, and pure infiniteness of the C*-algebras.

Computed K-theory for these monoid-related C*-algebras.

Developed a new method for K-theory computation in group C*-algebras.

Abstract

We study C*-algebras generated by left regular representations of right LCM one-relator monoids and Artin-Tits monoids of finite type. We obtain structural results concerning nuclearity, ideal structure and pure infiniteness. Moreover, we compute K-theory. Based on our K-theory results, we develop a new way of computing K-theory for certain group C*-algebras and crossed products.