Real reductive Cayley groups of rank 1 and 2.

A linear algebraic group G 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. [ABSTRACT FROM AUTHOR]