The paper classifies four invariant-theoretic regimes for non-reductive actions, proving divergence between finitely generated polynomial invariants and smooth invariants in discrete Lorentz and cocompact cases, thereby bounding the Hilbert-Weyl and Schwarz theorems via the role of properness.
Ueber die vollen invariantensysteme.Mathematische Annalen, 42:313–373, 1893
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Invariant theory for non-reductive actions: extensions of Hilbert and Schwarz theorems
The paper classifies four invariant-theoretic regimes for non-reductive actions, proving divergence between finitely generated polynomial invariants and smooth invariants in discrete Lorentz and cocompact cases, thereby bounding the Hilbert-Weyl and Schwarz theorems via the role of properness.