Geodesic
Complete Filtered Lie Algebras over a Vector Space of Dimension Two
Journal of Lie theory, Tome 12 (2002) no. 2, pp. 423-447
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There may exist many non-isomorphic complete filtered Lie algebras with the same graded algebra. In our previous paper "Complete filtered Lie algebras and the Spencer cohomology", J. Algebra 125 (1989) 66--109, we found elements in the Spencer cohomology that determined all complete filtered Lie algebras having certain graded algebra provided that obstructions do not exist in the cohomology at higher levels. In this paper we use the Spencer cohomology to classify all graded and filtered algebras over a real vector space of dimension two. 
@article{JLT_2002_12_2_JLT_2002_12_2_a6,
     author = {T. W. Judson},
     title = {Complete {Filtered} {Lie} {Algebras} over a {Vector} {Space} of {Dimension} {Two}},
     journal = {Journal of Lie theory},
     pages = {423--447},
     year = {2002},
     volume = {12},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2002_12_2_JLT_2002_12_2_a6/}
}
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T. W. Judson. Complete Filtered Lie Algebras over a Vector Space of Dimension Two. Journal of Lie theory, Tome 12 (2002) no. 2, pp. 423-447. http://geodesic.mathdoc.fr/item/JLT_2002_12_2_JLT_2002_12_2_a6/