Skip to Main content Skip to Navigation
Journal articles

Very nilpotent basis and n-tuples in Borel subalgebras

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.
Complete list of metadatas

Cited literature [5 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00660382
Contributor : Michael Bulois <>
Submitted on : Monday, January 16, 2012 - 3:13:01 PM
Last modification on : Wednesday, April 1, 2020 - 1:57:20 AM
Document(s) archivé(s) le : Tuesday, April 17, 2012 - 2:35:07 AM

Files

base_nilp.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Michael Bulois. Very nilpotent basis and n-tuples in Borel subalgebras. Comptes Rendus Mathématique, Elsevier Masson, 2011, 349 (3-4), pp.149-152. ⟨10.1016/j.crma.2010.12.005⟩. ⟨hal-00660382⟩

Share

Metrics

Record views

298

Files downloads

265