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

DOI10.1016/J.JALGEBRA.2012.11.023zbMATH Open1339.17007arXiv1105.5921OpenAlexW2962716931WikidataQ115351061 ScholiaQ115351061MaRDI QIDQ360153

Mouchira Zaiter

Publication date: 26 August 2013

Published in: Journal of Algebra (Search for Journal in Brave)

Abstract: 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 sualgebra. The main result of this paper is that N is a closed and irreducible subvariety of g x g, its normalisation has rational singularities and its normalization morphism is bijective.

Full work available at URL: https://arxiv.org/abs/1105.5921

zbMATH Keywords

Borel subalgebrasnormalizationinvariant polynomialsnullcone

Mathematics Subject Classification ID

Simple, semisimple, reductive (super)algebras (17B20) Root systems (17B22) Coadjoint orbits; nilpotent varieties (17B08)

Related Items (2)

Action on Grassmannians Associated with Commutative Semisimple Algebras ⋮ On varieties in an orbital variety closure in semisimple Lie algebras

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