REALIZATION OF A CLASS OF AFFINE LIE-SUPERALGEBRAS

In this paper, a class of affine Lie superalgebras is presented, whose Dynkin diagrams are constructed by, as usual, extending a Dynkin diagram D of Lie algebra (or superalgebra) by adding a node-psi that corresponds to the lowest root psi-0 of D. However, this added node-psi does not have the same degree as psi-0 in Z2 gradation (Z2=Z/2Z), i.e., psi-corresponds to an odd or even root as psi-0 corresponds to even or odd root. As far as we know, these Lie superalgebras did not appear in literature, and therefore we believe these are a new class of affine Lie superalgebras.