Moyal quantization and stable homology of necklace Lie algebras

Abstract

We 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 corrections

Cited by in corpus (1)

• Witt vectors. Part 1