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arXiv · 2601.07168

Jordan decompositions in Lie algebras and their duals

Loren Spice·Cheng-Chiang Tsai
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Abstract

We provide a discussion of Jordan decompositions in the Lie algebra, and the dual Lie algebra, of a reductive group in as uniform a way as possible. We give a counterexample to the claim that Jordan decompositions on the dual Lie algebra are unique, and state an upper bound on how non-unique they can be. We also prove some Chevalley-restriction-type claims about GIT quotients for the adjoint and co-adjoint actions of $G$.

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BibTeXRIS

Loren Spice, Cheng-Chiang Tsai. 2026-01-12. Jordan decompositions in Lie algebras and their duals. https://arxiv.org/abs/2601.07168

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