Functional Identities in Superalgebras: Theoretical Insights and Computational Verification

This paper investigates functional identities in superalgebras, building on Wang’s foundational work. We study d-superfree subsets and k-supercommuting maps in prime superalgebras, both with and without superinvolution, introducing new results on symmetric and skew elements. Using SageMath, we computationally verify key properties in the finite-dimensional superalgebra M2(Q), including supercommutators, superinvolutions, and k-supercommuting maps, thereby providing concrete illustrations of the abstract theory. These computations underscore the practical applicability of functional identities in finite-dimensional settings and offer fresh insights into superalgebra structures.