On the index of certain Lie algebras
Representation Theory
2007-05-23 v2
Abstract
We give an upper bound for the index of certain Lie algebras, called of seaweed type, introduced by V. Dergachev, A. Kirillov and D. Panyushev. We deduce from this a conjecture of D. Panyushev stated in "Inductive formulas for the index of seaweed Lie algebra, Moscow Math. Journal (2001) 221-241". We conjecture that our upper bound gives in fact a formula for the index of such Lie algebras, and we prove it in certain cases. Finally, we obtain a result concerning the index of parabolic subalgebras of a semisimple Lie algebra.
Keywords
Cite
@article{arxiv.math/0311104,
title = {On the index of certain Lie algebras},
author = {Patrice Tauvel and Rupert W. T. Yu},
journal= {arXiv preprint arXiv:math/0311104},
year = {2007}
}
Comments
This paper is written in French. There is an english abstract. This second version contains minor corrections