Cohomology of Lie-Conformal Algebras with Derivations  

作　　者：Shuangjian GUO 

机构地区：[1]School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guizhou 550025,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第6期754-768,共15页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12161013);the Basic Research Program(Natural Science)of Guizhou Province(Grant No.ZK[2023]025)。

摘　　要：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 introduce 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_(∞)-algebras and 2-derivations on conformal Lie 2-algebras.The category of 2-term conformal L_(∞)-algebras with homotopy derivations is equivalent to the category of conformal Lie 2-algebras with 2-derivations.

关 键 词：Lie conformal algebras COHOMOLOGY abelian extension conformal Lie 2-algebras homotopy derivation 

分 类 号：O152.5[理学—数学]