Universal C*-algebras generated by doubly non-commuting isometries

TL;DR

This paper constructs explicit representations of universal C*-algebras generated by doubly non-commuting isometries, demonstrating their embedding properties, nuclearity, and computing their K-theory, advancing understanding of their structure.

Contribution

It provides an explicit injective representation of these universal C*-algebras, enabling new insights into their embeddings, nuclearity, and K-theoretic properties.

Findings

Universal C*-algebras embed into each other

These algebras are nuclear

K-theory of these algebras is computed

Abstract

We give an explicit injective representation of the universal $\mathrm{C}^\ast$-algebra that is generated by doubly non-commuting isometries. This injectivity allows us to prove that such universal algebras embed naturally into each other and also, when combined with Rieffel's theory of deformation, to show that they are nuclear and to compute their K-theory.