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<p>Following the idea of Šemrl we introduce the notion of 2-local conformal derivations which generalizes conformal derivations in the sense of D’Andrea and Kac. In general it is difficult to determine 2-local conformal derivations except for the easiest case of Lie conformal algebras of rank one. We compute (2-local) conformal derivations of some Lie conformal algebras, including non-nilpotent solvable Lie conformal algebras of rank two, all finite simple Lie conformal algebras, and some finite semisimple Lie conformal algebras. Moreover, 2-local conformal derivations of semidirect sums of the Virasoro Lie conformal algebra with any current Lie conformal algebra are shown to be conformal derivations, and if the center of the Lie algebra of the current Lie algebra is zero then any conformal derivation is inner.</p>

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Conformal Derivations and 2-local Conformal Derivations of Lie Conformal Algebras

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Jia Lei,
  • Youjun Tan

摘要

Following the idea of Šemrl we introduce the notion of 2-local conformal derivations which generalizes conformal derivations in the sense of D’Andrea and Kac. In general it is difficult to determine 2-local conformal derivations except for the easiest case of Lie conformal algebras of rank one. We compute (2-local) conformal derivations of some Lie conformal algebras, including non-nilpotent solvable Lie conformal algebras of rank two, all finite simple Lie conformal algebras, and some finite semisimple Lie conformal algebras. Moreover, 2-local conformal derivations of semidirect sums of the Virasoro Lie conformal algebra with any current Lie conformal algebra are shown to be conformal derivations, and if the center of the Lie algebra of the current Lie algebra is zero then any conformal derivation is inner.