On related varieties to the commuting variety of a semisimple Lie algebra

JOURNAL OF ALGEBRA

卷:376

Article

Zaiter, Mouchira

关键词: Root systems;    Invariant polynomials;    Polarizations;    Borel subalgebras;    Nullcone;    Normalization;   

DOI  :  10.1016/j.jalgebra.2012.11.023

来源: Elsevier

【 摘 要 】

Let g be a semisimple Lie algebra of finite dimension. The nullcone N of g is the set of (x, y) in g x g such that x and y are nilpotents and are in the same Borel subalgebra. The main result of this paper is that N is a closed and irreducible subvariety of g x g and its normalization morphism is bijective. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free