Real reductive Cayley groups of rank 1 and 2

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.

24 pages. Igor Dolgachev is the author of Appendix A. New Appendix B contributed by the anonymous referee has been added. Final version, to appear in J. Algebra