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WHEN IS THE AUTOMORPHISM GROUP OF AN AFFINE VARIETY NESTED?

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Abstract

For an affine algebraic variety X, we study the subgroup Autalg(X) of the group of regular automorphisms Aut(X) of X generated by all the connected algebraic subgroups. We prove that Autalg(X) is nested, i.e., is a direct limit of algebraic subgroups of Aut(X), if and only if all the 𝔾a-actions on X commute. Moreover, we describe the structure of such a group Autalg(X).

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, 19 Bolshoy Karetny per, 127994, Moscow, Russia

    ALEXANDER PEREPECHKO

  2. Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russia

    ALEXANDER PEREPECHKO

  3. National Research University, Higher School of Economics, 20 Myasnitskaya ulitsa, Moscow, 101000, Russia

    ALEXANDER PEREPECHKO

  4. Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07737, Jena, Germany

    ANDRIY REGETA

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  1. ALEXANDER PEREPECHKO
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  2. ANDRIY REGETA
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Correspondence to ALEXANDER PEREPECHKO.

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Alexander Perepechko is supported by the Russian Foundation for Sciences (project no. 18-71-00153).

Andriy Regeta is partially supported by SNF (Schweizerischer Nationalfonds), project number P2BSP2 165390.

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PEREPECHKO, A., REGETA, A. WHEN IS THE AUTOMORPHISM GROUP OF AN AFFINE VARIETY NESTED?. Transformation Groups 28, 401–412 (2023). https://doi.org/10.1007/s00031-022-09711-1

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  • DOI: https://doi.org/10.1007/s00031-022-09711-1

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