We prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low dimension), there is a non-isomorphic filiform Lie bracket. This follows by constructing non-trivial linear deformations in a Zariski open dense set of the variety of filiform Lie algebras of dimension 9, 10 and 11 (in lower dimensions this is well known.)
1
CIEM-FaMAF, Universidad Nacional, Córdoba, Argentina
Paulo Tirao; Sonia Vera. There are No Rigid Filiform Lie Algebras of Low Dimension. Journal of Lie Theory, Tome 29 (2019) no. 2, pp. 391-412. http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a4/
@article{JOLT_2019_29_2_a4,
author = {Paulo Tirao and Sonia Vera},
title = {There are {No} {Rigid} {Filiform} {Lie} {Algebras} of {Low} {Dimension}},
journal = {Journal of Lie Theory},
pages = {391--412},
year = {2019},
volume = {29},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a4/}
}
TY - JOUR
AU - Paulo Tirao
AU - Sonia Vera
TI - There are No Rigid Filiform Lie Algebras of Low Dimension
JO - Journal of Lie Theory
PY - 2019
SP - 391
EP - 412
VL - 29
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a4/
ID - JOLT_2019_29_2_a4
ER -
%0 Journal Article
%A Paulo Tirao
%A Sonia Vera
%T There are No Rigid Filiform Lie Algebras of Low Dimension
%J Journal of Lie Theory
%D 2019
%P 391-412
%V 29
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a4/
%F JOLT_2019_29_2_a4
