FEIGIN AND ODESSKII'S ELLIPTIC ALGEBRAS

Abstract

This article summarizes some of the results in joint papers [CKS19, CKS21, CKS23] with Alex Chirvasitu and S. Paul Smith. We studied elliptic algebras introduced by Feigin and Odesskii in 1989, which are noncommutative graded algebras Qn, k(E, η) parametrized by an elliptic curve E, a point η ∈ E, and coprime positive integers n > k. These algebras are a generalization of Sklyanin algebras, recognized as important examples of Artin-Schelter regular algebras. One of our main results is that Qn, k(E, η) has the same Hilbert series as the polynomial ring in n variables when η is not a torsion point.