On the Commuting variety of a reductive Lie algebra

2012/06/25 by Jean-Yves Charbonnel, Charbonnel, Jean-Yves
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1206.5592

openalex publication_date 2012/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The commuting variety of a reductive Lie algebra \goth g is the underlying variety of a well defined subscheme of ≫ g. In this note, it is proved that this scheme is normal. In particular, its ideal of definition is a prime ideal.

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