On Morphisms Between Connected Commutative Algebraic Groups over a Field of Characteristic 0

verfasst von

Gabriel Andreas Dill

Abstract

Let K be a field of characteristic 0 and let G and H be connected commutative algebraic groups over K. Let Mor₀(G,H) denote the set of morphisms of algebraic varieties G → H that map the neutral element to the neutral element. We construct a natural retraction from Mor₀(G,H) to Hom(G,H) (for arbitrary G and H) which commutes with the composition and addition of morphisms. In particular, if G and H are isomorphic as algebraic varieties, then they are isomorphic as algebraic groups. If G has no non-trivial unipotent group as a direct factor, we give an explicit description of the sets of all morphisms and isomorphisms of algebraic varieties between G and H. We also characterize all connected commutative algebraic groups over K whose only variety automorphisms are compositions of automorphisms of algebraic groups with translations.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Transformation Groups

Band

29

Seiten

1389-1403

Anzahl der Seiten

15

ISSN

1083-4362

Publikationsdatum

12.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie, Geometrie und Topologie

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2107.14667 (Zugang: Offen)
https://doi.org/10.1007/s00031-022-09748-2 (Zugang: Offen)