2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112927We compute the stable homology of necklace Lie algebras associated with quivers and give a construction of stable homology classes from certain $A_\infty$-categories. Our construction is a generalization of the construction of homology classes of moduli spaces of curves due to M. Kontsevich. In the second part of the paper we produce a Moyal-type quantization of the symmetric algebra of a necklace Lie algebra. The resulting quantized algebra has natural representations in the usual Moyal quantization of polynomial algebras.Includes updated version of math.QA/0503405; second version contains minor correctionsQuantum Algebratext