A homotopy rigidity theorem for Ƶ 0 -stable C*-algebras

Key Points

• The research aims to establish a condition for the isomorphism of certain C*-algebras based on their homotopy equivalence without relying on the Universal Coefficient Theorem.
• Demonstrated that two simple, separable, nuclear, and Z0-stable C*-algebras are isomorphic if they are homotopy equivalent preserving traces.
• Developed the concept as a projectionless analogue to the rigidity theorem for Kirchberg algebras.
• Confirmed that being trace-preservingly homotopy equivalent leads to isomorphism for the specified C*-algebras.
• Highlighted implications for the broader understanding of rigidity in C*-theory without needing the Universal Coefficient Theorem.