@article{d8595a72da34404e81663d427c812164, title = "On Morphisms Between Connected Commutative Algebraic Groups over a Field of Characteristic 0", 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.", author = "Dill, {Gabriel Andreas}", note = "Funding Information: Open Access funding enabled and organized by Projekt DEAL. This work was supported by the Swiss National Science Foundation through the Early Postdoc.Mobility grant no. P2BSP2_195703. I thank the Mathematical Institute of the University of Oxford and my host there, Jonathan Pila, for hosting me as a visitor for the duration of this grant. During the final revisions of this manuscript, I was employed by the Leibniz Universit{\"a}t Hannover on the ERC grant of Ziyang Gao. Gabriel Dill has received funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement n 945714).", year = "2022", month = jul, day = "26", doi = "10.48550/arXiv.2107.14667", language = "English", journal = "Transformation Groups", issn = "1083-4362", publisher = "Birkhauser Boston", }