论文标题
对谎言代数的推导的概括
A generalization on derivations of Lie algebras
论文作者
论文摘要
我们在特征零的代数封闭场上，对有限维谎言代数的一系列新的广义推导进行研究。这种推导的新概括具有在关联素环理论中的类似物，并团结了许多众所周知的广义推导，这些衍生物已经广泛出现在Lie代数和其他非缔合代数的研究中。利用基本属性后，我们介绍和分析了它们的内部，尤其是关注相应的希尔伯特系列的合理性。在计算理想理论中应用技术，我们开发了一种方法，以明确计算复杂场上三维特殊线性谎言代数的这些新的广义推导。
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative prime rings and unites many well-known generalized derivations that have already appeared extensively in the study of Lie algebras and other nonassociative algebras. After exploiting fundamental properties, we introduce and analyze their interiors, especially focusing on the rationality of the corresponding Hilbert series. Applying techniques in computational ideal theory we develop an approach to explicitly compute these new generalized derivations for the three-dimensional special linear Lie algebra over the complex field.
