Vector bundles on elliptic curve and Sklyanin algebras

TL;DR

This paper explores the structure of vector bundles on elliptic curves and their relation to Sklyanin algebras, focusing on the algebraic and geometric properties of these objects in the context of elliptic curves and associative algebras.

Contribution

It introduces and analyzes the associative algebras $Q_{n,k}( ext{E}, au)$ associated with elliptic curves, revealing new connections between vector bundles and Sklyanin algebras.

Findings

Defined the algebras $Q_{n,k}( ext{E}, au)$ and their parameters

Established relationships between vector bundles on elliptic curves and Sklyanin algebras

Identified algebraic structures associated with elliptic curves and points $ au$

Abstract

In [4] we introduce the associative algebras $Q_{n,k}(\CE,\tau)$. Recall the definition. These algebras are labeled by discrete parameters $n,k$; $n,k$ are integers $n>k>0$ and $n$ and $k$ have not common divisors. Then, $\CE$ is an elliptic curve and $\tau$ is a point in $\CE$. We identify $\CE$ with $\BC/\Gamma$, where $\Gamma$ is a lattice.