论文标题
共形$ r $ -Matrix-Nijenhuis结构，Sympletic-Nijenhuis结构和$ \ Mathcal {O} n $结构
Conformal $r$-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and $\mathcal{O} N$-structures
论文作者
论文摘要
在本文中，我们首先研究了一个谎言条状代数的无限变形和带有一个模块的谎言条状代数（称为$ \ mathsf {lcmod} $配对），这导致了nijenhuis operator in lie Coldormal algebra和Nijenhuis结构的nijenhuis操作员的概念。然后，通过在Nijenhuis结构和$ \ Mathcal {O} $ - 运算符之间添加兼容性条件，我们介绍了$ \ Mathcal {o} n $结构的概念$ \ MATHCAL {O} $ - 运算符。特别是，我们表明兼容$ \ MATHCAL {O} $ - 谎言保串代数上的操作员可以由Nijenhuis操作员以谎言保形代数为特征。最后，我们介绍了在谎言保形代数上的保形$ r $ -r $ -Matrix-nijenhuis结构和符号 - nijenhuis结构，并研究其关系。
In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an $\mathsf{LCMod}$ pair), which lead to the notions of Nijenhuis operator on the Lie conformal algebra and Nijenhuis structure on the $\mathsf{LCMod}$ pair, respectively. Then by adding compatibility conditions between Nijenhuis structures and $\mathcal{O}$-operators, we introduce the notion of an $\mathcal{O} N$-structure on an $\mathsf{LCMod}$ pair and show that an $\mathcal{O} N$-structure gives rise to a hierarchy of pairwise compatible $\mathcal{O}$-operators. In particular, we show that compatible $\mathcal{O}$-operators on a Lie conformal algebra can be characterized by Nijenhuis operators on Lie conformal algebras. Finally, we introduce the notions of conformal $r$-matrix-Nijenhuis structure and symplectic-Nijenhuis structure on the Lie conformal algebra and study their relations.
