  It was shown that the spin chain model coming from AdS/CFT correspondence
satisfies the Yangian symmetry if we assume evaluation representation, though
so far there is no explicit proof that the evaluation representation satisfies
the Serre relation, which is one of the defining equations of the Yangian
algebra imposing constraints on the whole algebraic structure. We prove
completely that the evaluation representation adopted in the model satisfies
the Serre relation by introducing a three-dimensional gamma matrix. After
studying the Serre relation, we proceed to the whole Yangian algebraic
structure, where we find that the conventional construction of higher grade
generators is singular and we propose an alternative construction. In the
discussion of the higher grade generators, a great simplification for the proof
of the Serre relation is found. Using this expression, we further show that the
proof is lifted to the exceptional superalgebra, which is a non-degenerate
deformation of the original superalgebra.
