English

Elliptic Hall algebra on $\mathbb{F}_1$

Quantum Algebra 2017-08-30 v1 Algebraic Geometry

Abstract

We construct Hall algebra of elliptic curve over F1\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.

Keywords

Cite

@article{arxiv.1708.08881,
  title  = {Elliptic Hall algebra on $\mathbb{F}_1$},
  author = {Shintarou Yanagida},
  journal= {arXiv preprint arXiv:1708.08881},
  year   = {2017}
}
R2 v1 2026-06-22T21:26:53.460Z