论文标题
Rota-Baxter组的扩展和自动形态
Extensions and automorphisms of Rota-Baxter groups
论文作者
论文摘要
Rota-Baxter组的概念最近由Guo，Lang和Sheng [{\ em Adv。 Math。} 387（2021），107834，34 pp。]在Rota-Baxter Lie代数的几何研究中。正如Bardakov和Gubarev所观察到的那样，它们与偏斜的牙套密切相关。在本文中，我们通过构建合适的共同体学理论来研究Rota-Baxter组的扩展。除其他外，我们发现与偏斜牙套的扩展关系。考虑到Rota-baxter组的扩展，我们还构建了连接各种自动形态组的简短序列，该序列概括了井短精确的序列。
The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng [{\em Adv. Math.} 387 (2021), 107834, 34 pp.] in the geometric study of Rota-Baxter Lie algebras. They are closely related to skew braces as observed by Bardakov and Gubarev. In this paper, we study extensions of Rota-Baxter groups by constructing suitable cohomology theories. Among others, we find relations with the extensions of skew braces. Given an extension of Rota-Baxter groups, we also construct a short exact sequence connecting various automorphism groups, which generalizes the Wells short exact sequence.
