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Moyal quantization and stable homology of necklace Lie algebras

Victor Ginzburg·Travis Schedler
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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.

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Victor Ginzburg, Travis Schedler. 2006-09-05. Moyal quantization and stable homology of necklace Lie algebras. https://arxiv.org/abs/math/0605704

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