Vector bundles on elliptic curve and Sklyanin algebras

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.