Very nilpotent basis and n-tuples in Borel subalgebras
Representation Theory
2010-11-24 v2 Algebraic Geometry
Abstract
A (vector space) basis B of a Lie algebra is said to be very nilpotent if all the iterated brackets of elements of B are nilpotent. In this note, we prove a refinement of Engel's Theorem. We show that a Lie algebra has a very nilpotent basis if and only if it is a nilpotent Lie algebra. When g is a semisimple Lie algebra, this allows us to define an ideal of S((g^n)^*)^G whose associated algebraic set in g^n is the set of n-tuples lying in a same Borel subalgebra.
Keywords
Cite
@article{arxiv.1010.0821,
title = {Very nilpotent basis and n-tuples in Borel subalgebras},
author = {Bulois Michael},
journal= {arXiv preprint arXiv:1010.0821},
year = {2010}
}
Comments
short note, 4 pages