On the locality of formal distributions over pre-Lie and Novikov algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910763167252480 |
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| author | Bokut, L. A. Kolesnikov, P. S. |
| author_facet | Bokut, L. A. Kolesnikov, P. S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the locality of formal distributions over pre-Lie and Novikov algebras Bokut, L. A. Kolesnikov, P. S. Quantum Algebra 17B69, 17A30, 17A61 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. |
| title | On the locality of formal distributions over pre-Lie and Novikov algebras |
| topic | Quantum Algebra 17B69, 17A30, 17A61 |
| url | https://arxiv.org/abs/2404.17232 |