  In this note we propose a trilinear bracket formulation for the Hamiltonian
extended Magnetohydrodynamics (XMHD) model with homogeneous mass density. The
corresponding two-dimensional representation is derived by performing spatial
reduction on the three-dimensional bracket, upon introducing a symmetric
representation for the field variables. Subsequently, the trilinear bracket of
the resulting two-dimensional, four-field model is discretized using a finite
difference scheme, which results in semi-discrete dynamics that involve the
Arakawa Jacobian. Simulations of planar dynamics show that this scheme respects
the desired conservation properties to high precision.
