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arXiv · 2404.17232

On the locality of formal distributions over pre-Lie and Novikov algebras

L. A. Bokut·P. S. Kolesnikov
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Abstract

The Dong Lemma in the theory of vertex algebras states that the locality property of formal distributions over a Lie algebra is preserved under the action of a vertex operator. A~similar statement is known for associative algebras. We study local formal distributions over pre-Lie (right-symmetric), pre-associative (dendriform), and Novikov algebras to show that the analogue of the Dong Lemma holds for Novikov algebras but does not hold for pre-Lie and pre-associative ones.

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L. A. Bokut, P. S. Kolesnikov. 2024-04-26. On the locality of formal distributions over pre-Lie and Novikov algebras. https://arxiv.org/abs/2404.17232

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