Odd-quadratic Lie superalgebras with a weak filiform module as an odd part

The aim of this work is to study a very special family odd-quadratic Lie superalgebras g = 0 ¯ ⊕ 1 such that weak filiform -module (weak type). We introduce concept after having proved the unique non-zero superalgebra ( , B ) with abelian 2-dimensional dim . Let us note in context role center crucial. Thus, we obtain an inductive description type via generalized odd double extensions. Moreover, classification, up isomorphism, for smallest possible dimensions, is, six and eight.