Disjointness of a simple matrix Lie group and its Lie algebra

2022/07/26 by Larsen, Michael J.
#22E60 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2207.13209

Abstract

Let G be a connected closed subgroup of GL_n(ℂ) which is simple as a Lie group and which acts irreducibly on ℂⁿ. Regarding both G and its Lie algebra \mathfrakg as subsets of M_n(ℂ), we have G∩ \mathfrakg≠∅ if and only if G is a classical group and ℂⁿ is a minuscule representation.

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