报告题目：Reynolds algebras and their free objects from bracketed words and rooted trees

报 告 人：高兴 教授 兰州大学

报告时间：2020年12月10日 10:30-11:30

报告地点：腾讯会议：892522500

校内联系人：唐荣 tangrong@jlu.edu.cn

报告摘要：

The study of Reynolds algebras has its origin in the well-known work of O. Reynolds on fluid dynamics in 1895 and has since found broad applications. It also has close relationship with important linear operators such as algebra endomorphisms, derivations and Rota-Baxter operators. Many years ago G. Birkhoff suggested an algebraic study of Reynolds operators, including the corresponding free algebras. We carry out such a study in this talk. We first provide examples and properties of Reynolds operators, including a multi-variant generalization of the Reynolds identity. We then construct the free Reynolds algebra on a set. For this purpose, we identify a set of bracketed words called Reynolds words which serves as the linear basis of the free Reynolds algebra. A combinatorial interpretation of Reynolds words is given in terms of rooted trees without super crowns. The closure of the Reynolds words under concatenation gives the algebra structure on the space spanned by Reynolds words. Then a linear operator is defined on this algebra such that the Reynolds identity and the desired universal property are satisfied.

报告人简介：

高兴，博士，兰州大学教授、博士生导师。于2010年7月在兰州大学数学与统计学院获得博士学位，留校工作至今。在2015年8月至2016年8月间，在美国Rutgers大学交流访问，师从Rota-Baxter代数的国际领军人物郭锂教授。主要从事Rota-Baxter代数和代数组合等领域的研究， 在Journal of Algebra、 Journal of Pure and Applied Algebra 等国际期刊上发表SCI学术论文四十余篇。获甘肃省自然科学奖二等奖，主持数学天元基金、青年科学基金、国家自然科学基金面上项目和甘肃省自然科学基金项目, 曾参与国家自然科学基金项目2项和甘肃省自然科学基金项目1项，出版专著一本。