報告題目：Reynolds algebras and their free objects from bracketed words and rooted trees
報 告 人：高興 教授 蘭州大學
報告時間：2020年12月10日 10:30-11:30
報告地點：騰訊會議：892522500
校内聯系人：唐榮 tangrong@jlu.edu.cn
報告摘要：
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.
報告人簡介：
高興，博士，蘭州大學教授、博士生導師。于2010年7月在蘭州大學數學與統計學院獲得博士學位，留校工作至今。在2015年8月至2016年8月間，在美國Rutgers大學交流訪問，師從Rota-Baxter代數的國際領軍人物郭锂教授。主要從事Rota-Baxter代數和代數組合等領域的研究， 在Journal of Algebra、 Journal of Pure and Applied Algebra 等國際期刊上發表SCI學術論文四十餘篇。獲甘肅省自然科學獎二等獎，主持數學天元基金、青年科學基金、國家自然科學基金面上項目和甘肅省自然科學基金項目, 曾參與國家自然科學基金項目2項和甘肅省自然科學基金項目1項，出版專著一本。
