Details
| Original language | English |
|---|---|
| Pages (from-to) | 1389-1403 |
| Number of pages | 15 |
| Journal | Transformation Groups |
| Volume | 29 |
| Issue number | 4 |
| Early online date | 26 Jul 2022 |
| Publication status | Published - Dec 2024 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Geometry and Topology
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In: Transformation Groups, Vol. 29, No. 4, 12.2024, p. 1389-1403.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On Morphisms Between Connected Commutative Algebraic Groups over a Field of Characteristic 0
AU - Dill, Gabriel Andreas
N1 - Publisher Copyright: © 2022, The Author(s).
PY - 2024/12
Y1 - 2024/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85134811721&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2107.14667
DO - 10.48550/arXiv.2107.14667
M3 - Article
AN - SCOPUS:85134811721
VL - 29
SP - 1389
EP - 1403
JO - Transformation Groups
JF - Transformation Groups
SN - 1083-4362
IS - 4
ER -