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

Anzahl der Seiten

15

ISSN

1083-4362

Publikationsdatum

26.07.2022

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

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)