M. I. Kuznetsov refers to a 1-graded Lie algebra in "Simple modular Lie algebras with a solvable maximal subalgebra, Math. USSR Sb30 (1976), 68–76". Does he mean Z-graded?
it is not entirely clear but e.g. reference [3] of the paper in question mentions only graded Lie algebras while Kuznetsov speaks of 1-graded Lie algebras when referring to [3], so you may well be right. Perhaps you'd have better luck with the same question at http://mathoverflow.net
I think that "1-graded Lie algebra" just means "$\mathbb{Z}$-graded Lie algebra of depth 1". This seems to be consistent with the terminology used by the same author in other papers. For instance, in the paper "M.I. Kuznetov: Lie algebras with a subalgebra of codimension p . Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), no. 6, 1224–1247, 1439" the more general notion of q-graded Lie algebra is used with this meaning.
Thank you for your responses. I agree with your suggestion that the '1' refers to the depth would be consistent with what he writes, Salvatore.
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