论文标题
反式代数，Novikov代数和可交换的2儿童在谎言代数上
Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras
论文作者
论文摘要
lie代数上的抗pre-lie代数，Novikov代数和交通证的2个循环介绍了抗Pre-lie代数的概念，作为非高级交换的基本代数结构，这是“对称性”版本的“对称”形式，这是对谎言的“对称”形式。它们可以被描述为一类可遵守的代数，其负左乘法算子可以表示换向器的代数代数。我们观察到，反pre-lie代数与前代数之间有一个明显的比喻，可以从几个方面进行比较。此外，出乎意料的是，反学代数的子类，即接受的诺维科夫代数，以$ q $ -Algebras表示对应于Novikov代数。因此，从派生或更一般的可接受对的派生式代数中建造了可允许的诺维科夫代数。该对应关系扩展到泊松类型结构的水平，导致引入抗pre-lie Poisson代数和可允许的Novikov-Poisson代数的概念，而后者则对应于Novikov-Poisson代数。
Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebrasWe introduce the notion of anti-pre-Lie algebras as the underlying algebraic structures of nondegenerate commutative 2-cocycles which are the "symmetric" version of symplectic forms on Lie algebras. They can be characterized as a class of Lie-admissible algebras whose negative left multiplication operators make representations of the commutator Lie algebras. We observe that there is a clear analogy between anti-pre-Lie algebras and pre-Lie algebras by comparing them in terms of several aspects. Furthermore, it is unexpected that a subclass of anti-pre-Lie algebras, namely admissible Novikov algebras, correspond to Novikov algebras in terms of $q$-algebras. Consequently, there is a construction of admissible Novikov algebras from commutative associative algebras with derivations or more generally, admissible pairs. The correspondence extends to the level of Poisson type structures, leading to the introduction of the notions of anti-pre-Lie Poisson algebras and admissible Novikov-Poisson algebras, whereas the latter correspond to Novikov-Poisson algebras.
