Noncommutativity in bracketed $\mathcal{N} = 4$ S-wave theories and their algebraic decomposition

We study the noncommutativity of the $\mathcal{N} = 4$ S-wave theory in bracketed $\mathcal{N} = 4$ S-wave models by studying the algebraic decomposition of the noncommutative field equations in KK-deformed supersymmetric $\mathcal{N} = 4$ models. We find that the noncommutativity of the S-wave theory is an algebraic decomposition of the $\mathcal{N} = 4$ S-wave algebra.