Noncommutative Geometry Seminar

In this talk we will discuss, for $p \in [1,\infty)$ and an irrational number $\theta$, those Banach subalgebras of B(L^p) which are generated by two unitaries (invertible isometries) $u$ and $v$ subject to the usual commutation relation $uv = e^{2\pi i \theta}vu$. When $p$ is different from 2, it turns out that such an algebra is not unique, and the description of the possible norms is challenging. Our description allows us to show that all the L^p irrational rotation algebras are simple, have a unique trace, and have identical K-theory. Time permitting, we will discuss further topics such as embeddability into AF-algebras.