
Journal of Lie Theory 20 (2010), No. 3, 525541 Copyright Heldermann Verlag 2010 Graded Nilpotent Lie Algebras of Infinite Type Boris Doubrov Belarussian State University, Nezavisimosti av. 4, 220030 Minsk, Belarus doubrov@islc.org Olga Radko Institute of Mathematics, Surganova 11, 220072 Minsk, Belarus radko@islc.org The paper gives the complete characterization of all graded nilpotent Lie algebras with infinitedimensional 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 bracketgenerating distribution of constant type does not have nonzero complex weak characteristics, then its symmetry algebra is necessarily finitedimensional. The paper also contains a number of illustrative algebraic and geometric examples including the proof that any metabelian Lie algebra with a 2dimensional center always has an infinitedimensional Tanaka prolongation. Keywords: Graded nilpotent Lie algebras, Tanaka prolongation, metabelian Lie algebras, Lie algebra cohomology. MSC: 17B70, 53C30, 58A17 [ Fulltextpdf (198 KB)] for subscribers only. 