The Hamiltonian of an so(5) algebraic structure is constructed by extending an so(3) system to an so(5) dynamical system. We exactly solve the Hamiltonian by using the coherent state operator of the so(5) algebra. It is shown that the eigenstates corresponding to the same eigenvalue are multi-fold degenerate. The Berry connection associated with the so(5) coherent states is calculated and is found to be decomposed into Abelian and non-Abelian Berry connections. Based on the above theory, the Berry connections of the p-wave superconductivity model are determined explicitly
