In this survey article we describe some geometric results in the theory of noncommutative
rings and, more generally, in the theory of abelian categories. Roughly speaking and by …

The Koszul dual of a Sklyanin algebra A is a finite dimensional graded algebra depending
on an elliptic curve, a translation automorphism, and an integer n> 3; it may be defined as …

We consider algebras defined from quivers with relations that are kth order derivations of a
superpotential, generalizing results of Dubois-Violette to the quiver case. We give a …

Let k be an algebraically closed field, and let R be a finitely generated, connected graded k-
algebra, which is a domain of Gelfand-Kirillov dimension two. Write the graded quotient ring …

The 4-dimensional Sklyanin algebra is the homogeneous coordinate ring of a
noncommutative analogue of projective 3-space. The degree-two component of the algebra …

Conformal S1₂ enveloping algebras Page 1 Page 2 LE BRUYN 1 Introduction In
this paper we introduce and study a 3-parameter family of deformations of U(s12) which we call …

In this paper we prove a translation principle for the central quotients of four-dimensional
Sklyanin algebras, which is analogous to the translation principle for semi-simple Lie …

It is proved that there exists a scheme that represents the functor of line modules over a
graded algebra, and it is called the line scheme of the algebra. Its properties and its …

We consider graded Clifford algebras on n generators in the spirit of Artin, Tate and Van den
Bergh's non-commutative algebraic geometry. We give an algorithm for counting the point …

The four-dimensional Sklyanin algebras are certain noncommutative graded algebras
having the same Hilbert series as the polynomial ring on four indeterminates. Their structure …