Title: Elliptic Hall algebra on $\mathbb{F}_1$,
Abstract: We construct Hall algebra of elliptic curve over $\mathbb{F}_1$ using the
theory of monoidal scheme due to Deitmar and the theory of Hall algebra for
monoidal representations due to Szczesny. The resulting algebra is shown to be
a specialization of elliptic Hall algebra studied by Burban and Schiffmann.
Thus our algebra is isomorphic to the skein algebra for torus by the recent
work of Morton and Samuelson.