Stably Cayley semisimple groups.

  • Mikhail Borovoi

  • Boris Kunyavskii


A linear algebraic group GG over a field kk is called a Cayley group if it admits a Cayley map, i.e., a GG-equivariant birational isomorphism over kk between the group variety GG and its Lie algebra Lie(G)(G). A prototypical example is the classical "Cayley transform" for the special orthogonal group SOn\bold{SO}_n defined by Arthur Cayley in 1846. A linear algebraic group GG is called stably Cayley if G×SG \times S is Cayley for some split kk-torus SS. We classify stably Cayley semisimple groups over an arbitrary field kk of characteristic 0.