一、报告题目：Hom-(Lie) groups and the Yang- Baxter equation

二、报告人：陈良云 教授
三、时  间：2025年10月19日(周日)  10:40-11:40

四、地  点：A4-305

报告摘要：In this talk, we establish a connection between hom-groups and the Yang-Baxter equation, and classify finite idempotent hom-groups, finite regular hom-groups, simple regular hom-groups, simple regular hom-Lie groups, and simple regular hom-Lie algebras. Using the extension theory we developed and computer-assisted calculations, we classify low-order idempotent hom-groups. By analyzing the automorphism groups of hom-groups and their conjugacy classes, we classify regular hom-groups of relatively high orders. Employing tools from group theory, we almost completely classify finite simple regular hom-groups. Inspired by the classical classification methods of Lie groups, we establish a one-to-one correspondence between simply connected regular hom-Lie groups and regular hom-Lie algebras, thereby reducing the classification of simply connected simple regular hom-Lie groups to that of simple regular hom-Lie algebras. By applying classification techniques similar to those used for simple regular hom-groups, we almost completely classify simple regular hom-Lie algebras. Some classical theorems in group theory, such as Cauchy's theorem and Sylow's theorems, are also discussed within the framework of regular hom-groups.

报告人简介：陈良云，东北师范大学数学与统计学院三级教授、博士生导师、博士后合作导师。南开大学理学博士、哈尔滨工业大学博士后、东京大学博士后。吉林省拔尖创新人才、吉林省教育厅新世纪优秀人才、长春市有突出贡献专家，两门省级精品课负责人。主要研究方向是李超代数及其应用，主持国家自然科学基金5项和省部级项目6项，发表140余篇SCI论文，出版专著一部（科学出版社）。指导博士后12名、博士30名，硕士100余名。担任《山东大学学报》(理学版)《海南热带海洋学院学报》和10个外刊编委，国家重点研发计划“数学和应用研究”评审组专家、吉林省自然科学基金评审组专家等。

欢迎广大师生参加，联系人：孙钦秀