Geodesic
Graded Nilpotent Lie Algebras of Infinite Type
Journal of Lie theory, Tome 20 (2010) no. 3, pp. 525-541 Cet article a éte moissonné depuis la source Heldermann Verlag

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The paper gives the complete characterization of all graded nilpotent Lie algebras with infinite-dimensional Tanaka prolongation as extensions of graded nilpotent Lie algebras of lower dimension by means of a commutative ideal. We introduce a notion of weak characteristics of a vector distribution and prove that if a bracket-generating distribution of constant type does not have non-zero complex weak characteristics, then its symmetry algebra is necessarily finite-dimensional. The paper also contains a number of illustrative algebraic and geometric examples including the proof that any metabelian Lie algebra with a 2-dimensional center always has an infinite-dimensional Tanaka prolongation.
Classification : 17B70, 53C30, 58A17
Mots-clés : Graded nilpotent Lie algebras, Tanaka prolongation, metabelian Lie algebras, Lie algebra cohomology 
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     author = {B. Doubrov and O. Radko },
     title = {Graded {Nilpotent} {Lie} {Algebras} of {Infinite} {Type}},
     journal = {Journal of Lie theory},
     pages = {525--541},
     year = {2010},
     volume = {20},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_3_JLT_2010_20_3_a5/}
}
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B. Doubrov; O. Radko . Graded Nilpotent Lie Algebras of Infinite Type. Journal of Lie theory, Tome 20 (2010) no. 3, pp. 525-541. http://geodesic.mathdoc.fr/item/JLT_2010_20_3_JLT_2010_20_3_a5/