The Prime Snake Modules Of Type G₂

In this paper,we establish a connection between cluster algebras and a class of modules of the quantum affine algebra ??? of type G₂,which is called prime snake mod-ules.Firstly,we give the definition for prime snake modules of type G₂,and find the mutation sequences for the prime snake modules.Secondly,we find a system of equations for the prime snake modules.Finally,we show that the equations in the system of type G₂ correspond to mutations in some cluster algebra ???,moreover,every prime module in these equations corresponds to a cluster variable in some cluster algebra ???.