Quotients of degenerate Sklyanin algebras

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 three-dimensional Sklyanin algebra, a better way to view this using Heisenberg-invariants is shown.