Maximal commutative unipotent subgroups and a characterization of affine spherical varieties Article Swipe
Andriy Regeta
,
Immanuel van Santen
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.4171/jems/1651
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.4171/jems/1651
We describe maximal commutative unipotent subgroups of the automorphism group \mathrm{Aut}(X) of an irreducible affine variety X . Furthermore, we show that a group isomorphism \mathrm{Aut}(X) \allowbreak\to \mathrm{Aut}(Y) maps unipotent elements to unipotent elements, where Y is irreducible and affine. Using this result, we show that the automorphism group detects sphericity and the weight monoid.As an application, we show that an affine toric variety different from an algebraic torus is determined by its automorphism group among normal irreducible affine varieties, and we show that a smooth affine spherical variety different from an algebraic torus is determined by its automorphism group (up to an automorphism of the base field) among smooth irreducible affine varieties. This generalizes results obtained by Cantat, Kraft, Liendo, Urech, Xie and the authors.
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- Language
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- Landing Page
- https://doi.org/10.4171/jems/1651
- OA Status
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https://openalex.org/W4410213482Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.4171/jems/1651Digital Object Identifier
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Maximal commutative unipotent subgroups and a characterization of affine spherical varietiesWork title
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articleOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-05-08Full publication date if available
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Andriy Regeta, Immanuel van SantenList of authors in order
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https://doi.org/10.4171/jems/1651Publisher landing page
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YesWhether a free full text is available
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diamondOpen access status per OpenAlex
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https://doi.org/10.4171/jems/1651Direct OA link when available
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Unipotent, Mathematics, Affine transformation, Commutative property, Characterization (materials science), Pure mathematics, Commutative ring, Algebra over a field, Nanotechnology, Materials scienceTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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