This paper investigates the algebraic structure of the low-energy theory on parallel M2 branes, focusing on the non-abelian generalization of the M2 brane theory. The author starts by considering the supersymmetry transformations of the abelian case, derived from the Yang-Mills theory in 1+9 dimensions. The theory is then dualized to a scalar field, leading to the supersymmetry transformations of the M2 brane in SO(8) covariant form. The non-abelian generalization is explored by introducing an algebraic structure involving two sets of fields, A and B, with specific multiplication rules. The author proposes that the algebra is a semi-direct product of these sets, with three types of multiplications defined. These multiplications must satisfy certain properties, including antisymmetry and associativity, and must also satisfy Jacobi identities to ensure the closure of supersymmetry transformations. The author then considers the gauge transformations and their closure into a gauge algebra. The gauge field is treated differently from the scalars and fermions, as it is assumed to take values in an algebra B that closes on itself, while the scalars and fermions belong to a different set A. The author also discusses the dualization of the gauge field into a scalar field, which is necessary for the supersymmetry transformations to close. The author then considers the supersymmetry variations of the scalars, gauge field, and fermions, and finds that the closure of supersymmetry requires specific conditions on the parameters of the theory. The author also discusses the implications of these conditions for the gauge parameter and the supersymmetry variations of the fermionic equation of motion. The paper concludes with a discussion of the possible infinite-dimensional realization of the algebra, suggesting that the scalar fields could be non-abelian loops in transverse space. The author also speculates on the reduction of the M2 brane theory to the D2 brane theory, noting that the reduction is not yet fully understood. The paper also discusses the implications of the Chern-Simons term in the theory and the possible sign of the parameter ε, which determines the overall normalization of the action. The author concludes that the algebraic structure of the theory is essential for the closure of supersymmetry on the M2 branes.This paper investigates the algebraic structure of the low-energy theory on parallel M2 branes, focusing on the non-abelian generalization of the M2 brane theory. The author starts by considering the supersymmetry transformations of the abelian case, derived from the Yang-Mills theory in 1+9 dimensions. The theory is then dualized to a scalar field, leading to the supersymmetry transformations of the M2 brane in SO(8) covariant form. The non-abelian generalization is explored by introducing an algebraic structure involving two sets of fields, A and B, with specific multiplication rules. The author proposes that the algebra is a semi-direct product of these sets, with three types of multiplications defined. These multiplications must satisfy certain properties, including antisymmetry and associativity, and must also satisfy Jacobi identities to ensure the closure of supersymmetry transformations. The author then considers the gauge transformations and their closure into a gauge algebra. The gauge field is treated differently from the scalars and fermions, as it is assumed to take values in an algebra B that closes on itself, while the scalars and fermions belong to a different set A. The author also discusses the dualization of the gauge field into a scalar field, which is necessary for the supersymmetry transformations to close. The author then considers the supersymmetry variations of the scalars, gauge field, and fermions, and finds that the closure of supersymmetry requires specific conditions on the parameters of the theory. The author also discusses the implications of these conditions for the gauge parameter and the supersymmetry variations of the fermionic equation of motion. The paper concludes with a discussion of the possible infinite-dimensional realization of the algebra, suggesting that the scalar fields could be non-abelian loops in transverse space. The author also speculates on the reduction of the M2 brane theory to the D2 brane theory, noting that the reduction is not yet fully understood. The paper also discusses the implications of the Chern-Simons term in the theory and the possible sign of the parameter ε, which determines the overall normalization of the action. The author concludes that the algebraic structure of the theory is essential for the closure of supersymmetry on the M2 branes.