# The hyperrigidity of tensor algebras of C$^*$-correspondences

## TL;DR

This paper characterizes when tensor algebras of C*-correspondences are hyperrigid, providing necessary and sufficient conditions, especially for those arising from topological graphs, thus advancing understanding of their rigidity properties.

## Contribution

It offers a complete characterization of hyperrigidity for tensor algebras of C*-correspondences, including those from topological graphs, filling a gap in operator algebra theory.

## Key findings

- Necessary and sufficient conditions for hyperrigidity.
- Complete characterization for topological graph correspondences.
- Advances understanding of rigidity in tensor algebras.

## Abstract

Given a C$^*$-correspondence $X$, we give necessary and sufficient conditions for the tensor algebra $\mathcal T_X^+$ to be hyperrigid. In the case where $X$ is coming from a topological graph we obtain a complete characterization.