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.
1
Belarussian State University, Nezavisimosti av. 4, 220030 Minsk, Belarus
2
Institute of Mathematics, Surganova 11, 220072 Minsk, Belarus
Boris Doubrov; Olga 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/JOLT_2010_20_3_a5/
@article{JOLT_2010_20_3_a5,
author = {Boris Doubrov and Olga 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/JOLT_2010_20_3_a5/}
}
TY - JOUR
AU - Boris Doubrov
AU - Olga Radko
TI - Graded Nilpotent Lie Algebras of Infinite Type
JO - Journal of Lie Theory
PY - 2010
SP - 525
EP - 541
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a5/
ID - JOLT_2010_20_3_a5
ER -
%0 Journal Article
%A Boris Doubrov
%A Olga Radko
%T Graded Nilpotent Lie Algebras of Infinite Type
%J Journal of Lie Theory
%D 2010
%P 525-541
%V 20
%N 3
%U http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a5/
%F JOLT_2010_20_3_a5
