Noncommutative compact manifolds constructed from quivers

The moduli spaces of theta-semistable representations of a finite quiver can be packaged together to form a noncommutative compact manifold

A non-commutative topology on rep A

We extend the Zariski topology on simp A, the finite dimensional simple A-representations, to a non-commutative topology (in the sense of Fred Van Oystaeyen) on rep A, all finite dimensional A-representations, using Jordan-Holder filtrations. The non-commutativity of the topology is enforced by the order of the composition factors

The singularities of noncommutative manifolds

We present a faster method to determine all singularities of quiver moduli spaces up to smooth equivalence. We show that every quiver controls a large family of noncommutative compact manifolds

Noncommutative smoothness and coadjoint orbits

Raf Bocklandt and the author have proved in math.AG/0010030 that certain quotient varieties of representations of deformed preprojective algebras are coadjoint orbits for the necklace Lie algebra of the corresponding quiver. A conjectural ringtheoretical explanation of these results was given in terms of noncommutative smoothness in the sense of C. Procesi. In this paper we prove these conjectures. The main tool in the proof is the etale local description due to W. Crawley-Boevey in math.AG/0105247. Along the way we determine the smooth locus of the so called Marsden-Weinstein reductions for quiver representations

The superpotential XYZ+XZY+c3(X3+Y3+Z3)XYZ+XZY+\frac{c}{3}(X^3+Y^3+Z^3)

The motivic Donaldson-Thomas series associated to an elliptic Sklyanin algebra corresponding to a point of order two differs from the conjectured series in Conjecture 3.4 of 1510.08116