nLab William Crawley-Boevey

William Crawley-Boevey is an English mathematician, mainly algebraist. Topics he contributed to include representations of quivers, quiver varieties, Deligne-Simpson problem?, Kleinian singularities, double derivations.

• Webpage

• wikipedia:William_Crawley-Boevey; Google Scholar page

He introduced deformed preprojective algebras of quivers in connection with study of Kleinian singularities in

• W. Crawley-Boevey, Martin P. Holland, Noncommutative deformations of Kleinian singularities, Duke Math. J. 92 (3): 605–635 (1998) doi MR1620538

A construction generalizing deformed preprojective algebra of quivers and assigning to a $K$-algebra $A$ with an element $\lambda\in K\otimes_{\mathbf{Z}}K_0(A)$ a new algebra $\pi^\lambda(A)$ and a canonical homomorphism $A\to \pi^\lambda(A)$ is described in

• Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities, Comment. Math. Helv. 74 (1999) 548-574 doi

Flavour of noncommutative differential geometry based on double derivations:

• William Crawley-Boevey, Pavel Etingof, Victor Ginzburg, Noncommutative geometry and quiver algebras, Adv. Math. 209:1 (2007) 274-336 doi

Some papers

• Poisson structures on moduli spaces of representations, J. Algebra 325, 205–215 (2011) MR2745537 doi
• Geometry of the moment map for representations of quivers, Comp. Math. 126 (3): 257–293 doi MR1834739

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