A class of one-dimensional solvable extensions of the naturally graded filiform 3-Lie algebra NGF 5,3
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In this paper, we study one-dimensional solvable extensions of the naturally graded
filiform 3-Lie algebra NGF 5,3 . Using the description of derivations of the algebra NGF m,3 , we
determine the general form of the multiplication table of such extensions and derive the restrictions on
its parameters from the fundamental identity. The analysis naturally leads to two cases according to
the coefficients occurring in the product [x,e 1 ,e 2 ]. In the present paper, we consider in detail the case
α = β = 0. By applying suitable adapted changes of basis, the corresponding multiplication tables
are reduced to simpler forms and the remaining parameters are analyzed. The case (α,β) 6= (0,0)
is left for a separate investigation.
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