Sklyanin algebras revisited

TL;DR

This paper explores the relationship between Sklyanin algebras and noncommutative tori by establishing a functorial connection based on algebraic isomorphisms.

Contribution

It introduces a functor from elliptic curves to noncommutative tori, revealing a new algebraic correspondence through Sklyanin algebras.

Findings

Established an isomorphism between Sklyanin algebras and dense sub-algebras of noncommutative tori

Constructed a functor linking elliptic curves to noncommutative tori

Provided a new perspective on the algebraic structure of Sklyanin algebras

Abstract

We construct a functor from the category of elliptic curves to a category of noncommutative tori. Our proof is based on an isomorphism between the Sklyanin algebras and dense sub-algebras of the noncommutative tori.