Journal of Lie Theory

no. 3
Graded Nilpotent Lie Algebras of Infinite Type
Journal of Lie Theory, Volume 20 (2010) no. 3, pp. 525-541
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.
DOI: 10.5802/jolt.608
Classification: 17B70, 53C30, 58A17
Keywords: 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},
     doi = {10.5802/jolt.608},
     zbl = {1254.17025},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.608/}
}
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B. Doubrov; O. Radko. Graded Nilpotent Lie Algebras of Infinite Type. Journal of Lie Theory, Volume 20 (2010) no. 3, pp. 525-541. doi: 10.5802/jolt.608

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