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arXiv · 1010.0821

Very nilpotent basis and n-tuples in Borel subalgebras

Bulois Michael
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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.

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BibTeXRIS

Bulois Michael. 2010-10-05. Very nilpotent basis and n-tuples in Borel subalgebras. https://arxiv.org/abs/1010.0821

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