Algebraic embeddings of $\mathbb{C}$ into ${\text{SL}}_n(\mathbb{C})$

Abstract

We prove that any two algebraic embeddings of $\mathbb{C}$ into ${\text{SL}}_n(\mathbb{C})$ are the same up to an algebraic automorphism of ${\text{SL}}_n(\mathbb{C})$, provided that $n$ is at least $3$. Moreover, we prove that two algebraic embeddings of $\mathbb{C}$ into ${\text{SL}}_2(\mathbb{C})$ are the same up to a holomorphic automorphism of ${\text{SL}}_2(\mathbb{C})$.

10 pages, typos corrected, minor changes, improved exposition

References in corpus (2)

• Flexible varieties and automorphism groups
• Holomorphically Equivalent Algebraic Embeddings

Cited by in corpus (1)

• Uniqueness of Embeddings of the Affine Line into Algebraic Groups