论文标题
特征2
Hom-Lie superalgebras in characteristic 2
论文作者
论文摘要
本文的主要目的是在特征2中发展hom-lie Superalgebras的结构理论。我们讨论了它们的表示，半领产品，$α^k $衍生，并提供低维度的分类。我们介绍了特征2中对hom-lie代数的限制的另一个概念，这与圭恩和陈给出的概念不同。该定义的灵感来自于特征2中被限制的谎言代数的批准过程。我们还表明，特征2中的任何受限制的hom-lie代数都可以被纠正，从而引起hom-lie superalgebra。此外，我们在特征2中开发了hom-lie Superalgebras的共同体学理论，该理论提供了普通的谎言超级甲虫的共同体。此外，我们基于此共同学中的特征2中建立了hom-lie超甲虫的变形理论。
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, $α^k$-derivations and provide a classification in low dimension. We introduce another notion of restrictedness on Hom-Lie algebras in characteristic 2, different from one given by Guan and Chen. This definition is inspired by the process of queerification of restricted Lie algebras in characteristic 2. We also show that any restricted Hom-Lie algebra in characteristic 2 can be queerified to give rise to a Hom-Lie superalgebra. Moreover, we develop a cohomology theory of Hom-Lie superalgebras in characteristic 2, which provides a cohomology of ordinary Lie superalgebras. Furthermore, we establish a deformation theory of Hom-Lie superalgebras in characteristic 2 based on this cohomology.
