 Matrix-unit basis of the compact symplectic Lie algebra

In its block form, a matrix-unit basis of the unitary Lie algebra spans the anti-Hermitian block $A$, with the corresponding conjugate block below. Independent real and imaginary symmetric matrix units span $B$, with lower block $-\overline{B}$. These give $n^2+n(n+1)$ independent real generators, including diagonal symmetric entries.