Abstract: A linear algebraic group G  over a field k is called a Cayley group if it admits a Cayley map, i.e., a G-equivariant birational isomorphism over k between the group variety G and its Lie algebra Lie(G). A prototypical example is the classical "Cayley transform" for the special orthogonal group SO(n)  defined by Arthur Cayley in 1846. A linear algebraic group G is called stably Cayley if G \times S is Cayley for some split k-torus S (S=k^*\times ... \times k^*). For example, the special orthogonal group SO(n) is Cayley for any n>1 (Cayley). The special linear group  SL(n) over C is Cayley for n=2 (easy) and n=3 (Popov). For n>3 the group SL(n) is not Cayley because it is not stably Cayley (Lemire, Popov, Reichstein). I will discuss these notions and explain a new result (joint with Boris Kunyavskii): a classification of stably Cayley semisimple groups over an arbitrary field k of characteristic 0.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006