Uniqueness of Embeddings of the Affine Line into Algebraic Groups

Abstract

Let $Y$ be the underlying variety of a connected affine algebraic group. We prove that two embeddings of the affine line $\mathbb{C}$ into $Y$ are the same up to an automorphism of $Y$ provided that $Y$ is not isomorphic to a product of a torus $({\mathbb{C}}^{\ast }{)}^k$ and one of the three varieties ${\mathbb{C}}^3$, ${\mathrm{SL}}_2$, and ${\mathrm{PSL}}_2$.

37 pages, comments welcome

References in corpus (2)

• Flexible varieties and automorphism groups
• Algebraic embeddings of $\mathbb{C}$ into ${\text{SL}}_n(\mathbb{C})$