Discussion on a class of generalized cluster algebras
Cluster algebra is an important research object in algebra.Cluster algebra is a kind of com-mutative subalgebra of a rational function field which satisfies some mutation rule by taking cluster variables as generators.There are some research results on the cluster algebra A(b,c)of rank 2.In particular,when bc ≤4,A(b,c)is of two types of algebras with finite type and affine type.Nowa-days,cluster algebra plays an important role in Poisson geometry,representation theory,quantum group and other research fields.This paper studies the algebraic structure of a special class of general-ized cluster algebras,mainly by defining sn(n ≥1)to establish the multiplication formula of such gen-eralized cluster algebras,and thus proves that the set of all cluster monomials xpmxqm+1(m ∈ Z)and sn(n≥1)is an integer base of such generalized cluster algebras.
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维普
