The Matrix Representations of Centroids for Low‐Dimensional Mock‐Lie Algebras.

Mock‐Lie algebras, a unique class of commutative algebras that satisfy the Jacobi identity, are gaining attention for their potential applications in various mathematical contexts. This study presents a matrix representation of the centroid for Mock‐Lie algebras in dimensions up to four, offering insights into their structure and interactions. By applying the centroid concept and utilizing matrix operations, we explore the relationships between matrix elements, leading to a better understanding of these algebras. Our findings aim to contribute to the growing interest in Mock‐Lie algebras and their role within the broader algebraic landscape. [ABSTRACT FROM AUTHOR]