{
  "annotation_id": "6ed7a0b0-05d6-41f0-b0f0-81a81c1f808d",
  "date_created": "2026-02-17T05:53:12.438000Z",
  "date_modified": "2026-02-17T05:53:12.438000Z",
  "file_hash": "ce47b5051099bc20c6aa0fa72f3320b3a48adfda60eafcda00fe6f5eb80e6c3a",
  "private": false,
  "record": {
    "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"
    ],
    "categories": [
      "math.RT",
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Jordan decompositions in Lie algebras and their duals",
    "url": "https://arxiv.org/abs/2601.07168",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "229ffb7d-eb21-4adc-a577-76fae7a7663f",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}