Varieties of elementary subalgebras of submaximal rank in type A

2017/07/03 by Yang Pan, Pan, Yang
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1707.00446

openalex publication_date 2017/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected simple algebraic group over an algebraically closed field k of characteristic p > 0, and g := Lie(G). We additionally assume that G is standard and is of type An. Motivated by the investigation of the geometric properties of the varieties E(r, g) of r-dimensional elementary subalgebras of a restricted Lie algebra g, we will show in this article the irreducible components of E(rkp(g)-1,g) when rkp(g) is the maximal dimension of an elementary subalgebra of g.

Related

• Elementary Subalgebrs of Lie Algebras
• Elementary subalgebras of Lie algebras
• Varieties of elementary subalgebras of maximal dimension for modular Lie algebras
• Varieties of elements of given order in simple algebraic groups
• Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic