Abstract. The representation scheme rep n A of the 3-dimensional Sklyanin algebra A associated to a plane elliptic curve and n-torsion point contains singularities over the augmentation ideal m. We investigate the semi-stable representations of the noncommutative blow-up algebra B = A⊕mt⊕m 2 t 2 ⊕. . . to obtain a partial resolution of the central singularitysuch that the remaining singularities in the exceptional fiber determine an elliptic curve and are all of type C × C 2 /Zn.

We show that the reduced point variety of a quantum polynomial algebra is the union of specific linear subspaces in $\mathbb{P}^n$, we describe its irreducible components and give a combinatorial description of the possible configurations in small dimensions.Comment: 10 pages, an extended version of arxiv.org/abs/1506.0651

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.

Abstract. In this article, a new proof is given of the description of the center of quadratic Sklyanin algebras of global dimension three and four and the center of cubic Sklyanin algebras of global dimension three. The representation theory of the Heisenberg groups H 2 , H 3 and H 4 will play an important role. In addition a new proof is given of Van den Bergh's result regarding noncommutative quadrics.