<![CDATA[Lie algebra is one of the important algebraic structures in mathematics, particularly in the study of symmetry and the representation of algebraic structures. Recent developments have established Lie algebra constructions on genetic codes by defining the set of DNA bases as a finite field and representing codons as a vector space. The Lie bracket is a binary operation that characterizes the structural interaction within a Lie algebra, specifically by satisfying bilinearity, antisymmetry, and the Jacobi identity. Building upon this definition, the objective of this research is to develop another representation of the Lie bracket within the codon space while maintaining the essential axioms that define a Lie algebra structure. The method employed is qualitative research using a constructive experimental approach to define a specific operation based on existing structures, followed by a formal proof to ensure the operation satisfies all Lie algebra axioms. This research utilizes the Lie bracket structure established by Sánchez et al. on the space $B^3$ and applies an invertible linear transformation to derive an alternative form, as this method effectively preserves the essential algebraic properties while allowing for structural variation. The operation constructed through this transformation satisfies all Lie algebra axioms, confirming the formation of a valid and structurally consistent Lie bracket. These findings confirm that the Lie bracket structure on the codon space is not unique and still offers opportunities for further development in various similar forms.]]>
