Moyal quantization and stable homology of necklace Lie algebras

Details Moyal quantization and stable homology of necklace Lie algebras Moyal quantization and stable homology of necklace Lie algebras

2006-05-28

arxiv.org/abs/math/0605704v2

Mathematics

Quantum Algebra

Includes updated version of math.QA/0503405; second version contains minor corrections

Scientific paper

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.

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