2010/01/03 by Doubrov, Boris, Radko, Olga
#17B70 #53C30 #58A17 #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1001.0379
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.