Let $\theta \in \mathbb{R}\backslash\mathbb{Q}$. The irrational rotation C\*-algebra $\mathcal{A}\_{\theta}$ is the universal C\*-algebra generated by unitary elements $u$ and $v$ with $vu=e^{2\pi i \theta}uv$.


What is the spectrum of u+v?


(Note: in the case where the unitary elements u and v are the standard generators of a free group factor, the spectrum of u+v is computable by work of Haagerup and Larsen.)



Spectrum of the sum of generators for irrational rotation algebra
The question is nicely resolved here: <http://arxiv.org/abs/1210.4771>


