Sequences of Z2⊗Z2 graded Lie algebras and superalgebras

Applying methods similar to those used for classical Lie superalgebras (Z2 graded algebras), we construct sequences of Z2⊕Z2 graded Lie superalgebras. In this way one obtains the spl(m,n,r,s), osp(m,n,r,s), P1(m,r), P3(m,n), ospP3(m,n), P1,2(m), and Q (m) series. We also give series of Z2⊕Z2 graded Lie algebras. Closed forms for superdeterminants and determinants of Z2⊕Z2 graded matrices are presented.