In recent years, the representation theory of quivers has enjoyed an enormous impact of new techniques both from algebraic geometry and from quantum group theory. Some examples of this are the realization of quantum, groups in terms of the representation theory of quivers via C. M. Ringel's Hall algebra approach [62, 23], G. Lusztig's geometric interpretation of the Hall algebra approach [50, 51, 52] and H. Nakajima's work on quiver varieties [56, 57].
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