»ã±¨±êÌâ (Title)£ºOn Galois-like theory of cluster algebras and some examples from surfaces

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»ã±¨ÌáÒª£º 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.