群上的Rota-Baxter算子
Rota-Baxter operators on groups
AI总结：
针对群上Rota-Baxter算子这一近年定义的概念，本文提供其一般构造方法，研究映射扩展问题，揭示与关联李环上算子的联系，并描述散在单群上的算子。
摘要：
环与代数上的Rota-Baxter算子理论自1960年起得到发展。近期，L. Guo、H. Lang、Y. Sheng在[arXiv:2009.03492]中定义了群上Rota-Baxter算子的概念。我们提供群上Rota-Baxter算子的若干一般构造方法，研究群上给定映射向Rota-Baxter算子的扩展问题，阐述群上Rota-Baxter算子与关联李环上Rota-Baxter算子的联系，并描述散在单群上的Rota-Baxter算子。
英文摘要：
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of Rota-Baxter operators on a group. Given a map on a group, we study its extensions to a Rota-Baxter operator. We state the connection between Rota-Baxter operators on a group and Rota-Baxter operators on an associated Lie ring. We describe Rota-Baxter operators on sporadic simple groups.
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