论文标题
$ \ MATHCAL {O} $ - 运算符和nijenhius运算符
$\mathcal{O}$-operators and Nijenhius operators of associative conformal algebras
论文作者
论文摘要
我们研究$ \ MATHCAL {O} $ - 关于共形双模模的联想保形代数的操作员。作为$ \ Mathcal {O} $ - 运算符和Dendriform保形代数的天然概括，我们介绍了扭曲的Rota-Baxter运算符和共形NS-Elgebras的概念。我们表明，扭曲的rota-baxter操作员会产生共形NS-Elgebras，与$ \ MATHCAL {O} $ - 操作员诱导Dendriform Crompormal代数相同。我们介绍了协会尼尼修斯操作员的共形类似物，并列举了主要特性。通过使用Kosmann-Schwarzbach的派生支架构造和Uchino方法，我们获得了一个分级的Lie代数，其Maurer-Cartan元素由$ \ Mathcal {O} $ - 运算符提供。这使我们能够构建$ \ Mathcal {O} $ - 运算符的共同体。该协同学可以看作是在合适的保形双模块中具有系数的关联保形代数的Hochschild共同体。
We study $\mathcal{O}$-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of $\mathcal{O}$-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter operators and conformal NS-algebras. We show that twisted Rota-Baxter operators give rise to conformal NS-algebras, the same as $\mathcal{O}$-operators induce dendriform conformal algebras. And we introduce a conformal analog of associative Nijenhius operators and enumerate main properties. By using derived bracket construction of Kosmann-Schwarzbach and a method of Uchino, we obtain a graded Lie algebra whose Maurer-Cartan elements are given by $\mathcal{O}$-operators. This allows us to construct cohomology of $\mathcal{O}$-operators. This cohomology can be seen as the Hochschild cohomology of an associative conformal algebra with coefficients in a suitable conformal bimodule.
