Ad-nilpotent ideals of a parabolic subalgebra

JOURNAL OF ALGEBRA

卷:319

Article

Righi, Celine

关键词: ad-nilpotent ideal;    abelian ideal;    parabolic subalgebra;    Lie algebra;   

DOI  :  10.1016/j.jalgebra.2007.11.005

来源: Elsevier

【 摘 要 】

We extend the results of Cellini and Papi [P. Cellim, P. Papi, Ad-nilpotent ideals of a Borel subalgebra, J. Algebra 225 (2000) 130-140; P. Cellini, P. Papi, Ad-nilpotent ideals of a Bore] subalgebra II, J. Algebra 258 (2002) 112-121] on the characterizations of ad-nilpotent and abelian ideals of a Borel subalgebra to parabolic subalgebras of a simple Lie algebra. These characterizations are given in terms of elements of the affine Weyl group and faces of alcoves. In the case of a parabolic subalgebra of a classical simple Lie algebra, we give formulas for the number of these ideals. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free