Real reductive Cayley groups of rank 1 and 2

TL;DR

This paper classifies real reductive algebraic groups of rank 1 and 2 that admit a Cayley map, providing a complete understanding of which such groups are Cayley over the real numbers.

Contribution

The paper offers a classification of real reductive Cayley groups of rank 1 and 2, expanding the understanding of Cayley maps in algebraic groups.

Findings

Classified all rank 1 and 2 real reductive Cayley groups.

Identified specific conditions under which these groups admit Cayley maps.

Enhanced the understanding of Cayley groups in the context of real algebraic groups.

Abstract

A linear algebraic group G is over a field K is called a Cayley K-group if it admits a Cayley map, i.e., a G-equivariant K-birational isomorphism between the group variety G and its Lie algebra. We classify real reductive algebraic groups of absolute rank 1 and 2 that are Cayley R-groups.