On classical Z2×Z2-graded Lie algebras

Abstract

We construct classes of Z2×Z2-graded Lie algebras corresponding to the classical Lie algebras in terms of their defining matrices. For the Z2×Z2-graded Lie algebra of type A, the construction coincides with the previously known class. For the Z2×Z2-graded Lie algebra of types B, C, and D, our construction is new and gives rise to interesting defining matrices closely related to the classical ones but undoubtedly different. We also give some examples and possible applications of parastatistics.