  We discuss the integrable boundary conditions for the one-dimensional (1D)
Hubbard Model in the framework of the Quantum Inverse Scattering Method (QISM).
We use the fermionic R-matrix proposed by Olmedilla et al. to treat the twisted
periodic boundary condition and the open boundary condition. We determine the
most general form of the integrable twisted periodic boundary condition by
considering the symmetry matrix of the fermionic R-matrix. To find the
integrable open boundary condition, we shall solve the graded reflection
equation, and find there are two diagonal solutions, which correspond to a) the
boundary chemical potential and b) the boundary magnetic field. Non-diagonal
solutions are obtained using the symmetry matrix of the fermionic R-matrix and
the covariance property of the graded reflection equation. They can be
interpreted as the SO(4) rotations of the diagonal solutions.
