On the locality of formal distributions over right-symmetric and Novikov algebras

L. A. Bokut   ; P. S. Kolesnikov

The Bulletin of Irkutsk State University. Series Mathematics, Tome 50 (2024), pp. 83-100

Résumé

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.

Détail

Mots-clés : conformal algebra
Keywords: locality function, pre-Lie algebra, Novikov algebra.

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