The Z2×Z2-graded general linear Lie superalgebra

We present a novel realization of the Z2×Z2-graded Lie superalgebra gl(m1,m2|n1,n2) inside an algebraic extension of the enveloping algebra of the Z2-graded Lie superalgebra gl(m|n), with m = m + m and n = n + n. A consequence of this realization is that the representations of gl(m|n) "lift up" to representations of gl(m1,m2|n1,n2), with matrix elements differing only by a sign, which we are able to characterize concisely