Quotients of degenerate Sklyanin algebras

TL;DR

This paper explores how the Heisenberg group of order 27 can be used to construct quotients of degenerate Sklyanin algebras, revealing properties similar to classical Sklyanin algebras and providing new insights into their central elements.

Contribution

It introduces a novel method using the Heisenberg group to analyze quotients of degenerate Sklyanin algebras, highlighting their structural similarities and invariants.

Findings

Quotients share the same Hilbert series as classical Sklyanin algebras

They have the same character series

Existence of a central element of degree 3

Abstract

In this paper it is shown how the Heisenberg group of order 27 can be used to construct quotients of degenerate Sklyanin algebras. These quotients have properties similar to the classical Sklyanin case in the sense that they have the same Hilbert series, the same character series and a central element of degree 3. Regarding the central element of a 3-dimensional Sklyanin algebra, a better way to view this using Heisenberg-invariants is shown.