勷勤数学•专家报告

题      目：Restricted post-Lie algebras and restricted Rota-Baxter Lie algebras

报  告  人： 黎允楠 副教授  (邀请人：张泽锐)

                                  广州大学

时      间： 7月13日  11：00-12:00

地     点：数科院东楼401

报告人简介:

       黎允楠，广州大学数学与信息科学学院副教授，硕士生导师，博士毕业于华东师范大学数学系，研究方向为李代数、量子群与代数组合，现与合作者在 Math. Z.,  Ann. Mat. Pura Appl., Forum Math., Pacific J. Math., J. Noncommut. Geom., J. Algebra, J. Pure Appl. Algebra, J. Combin. Theory Ser. A 等数学期刊发表论文二十余篇，主持完成国家、广东省自然科学基金面上项目各 1 项，另主持在研广东省自然科学基金面上项目 1 项。2018-2019 国家公派美国罗格斯大学研修访问，2020 年认定为广州市青年后备人才，曾受邀为 Adv. Math., European J. Combin., J. Algebraic Combin., Ramanujan J., Front. Math. China 等数学期刊审稿。

摘      要：

       Recently Ehret and Gilliers introduced the notion of (trivially) restricted post-Lie algebras, as an analogue of restricted Lie and restricted pre-Lie algebras. % in \cite{EG}.

In this talk, we especially introduce restricted Rota-Baxter Lie algebras of arbitrary weight together with an intrinsic graph subalgebra characterization, and show that they induce restricted post-Lie algebras by the splitting property, and also have the novel replication property.

Then we provide two natural constructions of these restricted Rota-Baxter objects respectively from Rota-Baxter associative algebras of arbitrary weight and Rota-Baxter Lie algebras of weight $1$ in prime characteristic. This is based on a joint work with Ke Ou.

          欢迎老师、同学们参加、交流！