dorsal/arxiv
View SchemaJordan decompositions in Lie algebras and their duals
| Authors | Loren Spice, Cheng-Chiang Tsai |
|---|---|
| Categories | |
| ArXiv ID | 2601.07168vv1 |
| URL | https://arxiv.org/abs/2601.07168 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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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"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 $G$.",
"arxiv_id": "2601.07168",
"authors": [
"Loren Spice",
"Cheng-Chiang Tsai"
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"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Jordan decompositions in Lie algebras and their duals",
"url": "https://arxiv.org/abs/2601.07168",
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