汇报标题 (Title)：On Galois-like theory of cluster algebras and some examples from surfaces
（关于簇代数的类伽罗瓦理论及曲面上的一些例子）
汇报人 (Speaker)：李方教授（同济大学）
汇报功夫 (Time)：2025年11月29日（周六）9:00-9:50
汇报地址 (Place)：校本部F309
约请人(Inviter)：黄红娣
主办部门：理学院数学系
汇报提要： One of the key-points in Galois theory via field extensions is to build up a correspondence between subfields of a field and subgroups of its automorphism group, so as to study fields via methods of groups. As an analogue of the Galois theory, we study the relations between cluster subalgebras of a cluster algebra and subgroups of its automorphism group and then to set up the Galois-like method. As examples, we characterize the cluster automorphism group of cluster algebras from feasible surfaces. For the kind of cluster algebras, as the answers of two conjectures
given in the first part, we prove the rank invariants of maximal cluster subalgebras under action of subgroups of the cluster automorphism group of such a cluster algebra and moreover construct the descending series of cluster subalgebras via an ascending series of subgroups. This work is joint with Jinlei Dong.
