This paper explores the algebraic structures that emerge when closing supersymmetry on parallel M2 branes, following the suggestion of incorporating a gauge field with topological degrees of freedom. The author investigates a non-abelian generalization of the low-energy theory living on a single M2 brane, inspired by the work of Bagger and Lambert. The starting point is the assumption that supersymmetry can be realized on fields with a Lorentz index structure, without needing to know the internal structure in detail. The fields are assumed to take values in an algebra, with specific multiplication rules that ensure closure under supersymmetry transformations. The paper begins by reviewing the abelian case, where the supersymmetry transformations are derived from the Yang-Mills action on a single D2 brane. It then moves to the non-abelian case, where the algebra is assumed to be a semi-direct product of two sets, \(\mathcal{A}\) and \(\mathcal{B}\), with specific multiplication rules. The author proposes a realization of this algebra using gamma matrices and discusses the gauge covariant derivative and the gauge transformations. The paper also explores the closure of supersymmetry transformations for scalars, the gauge field, and fermions, showing that the equations of motion are gauge invariant. It suggests that the gauge field is a new field, not derived from the Yang-Mills theory, and that the fermions are non-abelian loops in superspace. The author concludes by speculating on an infinite-dimensional realization of the algebra, where the scalar fields are non-abelian loops in transverse space, and the gauge field is an ordinary flat gauge field. The paper includes a section on gamma matrix identities and acknowledges the contributions of N. Lambert, N. Copland, and U. Gran.This paper explores the algebraic structures that emerge when closing supersymmetry on parallel M2 branes, following the suggestion of incorporating a gauge field with topological degrees of freedom. The author investigates a non-abelian generalization of the low-energy theory living on a single M2 brane, inspired by the work of Bagger and Lambert. The starting point is the assumption that supersymmetry can be realized on fields with a Lorentz index structure, without needing to know the internal structure in detail. The fields are assumed to take values in an algebra, with specific multiplication rules that ensure closure under supersymmetry transformations. The paper begins by reviewing the abelian case, where the supersymmetry transformations are derived from the Yang-Mills action on a single D2 brane. It then moves to the non-abelian case, where the algebra is assumed to be a semi-direct product of two sets, \(\mathcal{A}\) and \(\mathcal{B}\), with specific multiplication rules. The author proposes a realization of this algebra using gamma matrices and discusses the gauge covariant derivative and the gauge transformations. The paper also explores the closure of supersymmetry transformations for scalars, the gauge field, and fermions, showing that the equations of motion are gauge invariant. It suggests that the gauge field is a new field, not derived from the Yang-Mills theory, and that the fermions are non-abelian loops in superspace. The author concludes by speculating on an infinite-dimensional realization of the algebra, where the scalar fields are non-abelian loops in transverse space, and the gauge field is an ordinary flat gauge field. The paper includes a section on gamma matrix identities and acknowledges the contributions of N. Lambert, N. Copland, and U. Gran.