We study preprojective algebras of graphs and their relationship to module categories over representations of quantum SL ( 2 ). As an application, ADE quiver varieties of Nakajima are shown to be subvarieties of the variety of representations of a certain associative algebra introduced by Lusztig. © 2005 Elsevier Inc. All rights reserved.
Malkin, A., Ostrik, V., & Vybornov, M. (2006). Quiver varieties and Lusztig’s algebra. Advances in Mathematics, 203(2), 514–536. https://doi.org/10.1016/j.aim.2005.05.002