The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I indroduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that make it the su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the transfer matrix commutes with the hamiltonian. While the model is integrable in one dimension, it provides a generalization of the Hubbard hamiltonian in any dimension.
The extended Hubbard model with on-site interaction U and nearest-neighbor interaction V/d is studied at half filling in high dimensions (d\ensuremath{\gg}1). At small U and V the critical temperature and the order parameter are calculated including the 1/d corrections. The results differ from those obtained in the Hartree approximation by a factor of order unity.$---- At V/U=1/2 a transition is found from an antiferromagnetic to a charge-density-wave phase. A similar transition is found at large U and V, suggesting that the transition is present for all U and V satisfying V/U=1/2.