15 citations · 43 across the 5 of their papers we have counts for
10 papers
A note on noncommutative Poisson structures
William Crawley-Boevey
We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebra…
A note on sub-bundles of vector bundles
William Crawley-Boevey, Bernt Tore Jensen
It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We giv…
Noncommutative Geometry and Quiver algebras
William Crawley-Boevey, Pavel Etingof, Victor Ginzburg
We develop a new framework for noncommutative differential geometry based on double derivations. This leads to the notion of moment map and of Hamiltonian reduction in noncommutati…
Multiplicative preprojective algebras, middle convolution and the Deligne-Simpson problem
William Crawley-Boevey, Peter Shaw
We introduce a family of algebras which are multiplicative analogues of preprojective algebras, and their deformations, as introduced by M. P. Holland and the first author. We show…
Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity
William Crawley-Boevey
We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of c…
Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)
William Crawley-Boevey, Michel Van den Bergh
A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has posi…