Cohomology of Lie-conformal algebras with derivations
Received:December 14, 2023  Revised:March 04, 2024
Key Words: Lie conformal algebras   cohomology   abelian extension   conformal Lie 2-algebras   homotopy derivation  
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Shuangjian Guo* Guizhou University of Finance and Economics Huaxi University Town, Guiyang, Guizhou Province
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Abstract:
      In this paper, we consider Lie conformal algebras with derivations. A pair consisting of a Lie conformal algebra and a distinguished derivation is called a LieCDer pair. We define a cohomology theory for LieCDer pair with coefficients in a representation. Furthermore, we study abelian extensions of a LieCDer pair as an application of cohomology theory. Finally, we consider homotopy derivations on 2-term conformal L$_{\infty}$-algebras and 2-derivations on conformal Lie 2-algebras. The category of 2-term conformal L$_{\infty}$-algebras with homotopy derivations is equivalent to the category of conformal Lie 2-algebras with 2-derivations.
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