**Mikhail Borovoi**

Tel Aviv University , Israel

February 15, 2018

** Cayley groups**:
I will start the talk from the classical "Cayley transform" for the
special orthogonal group SO(n) defined by Arthur Cayley in 1846. A
connected linear algebraic group G over C is called a *Cayley group* if it admits a *Cayley map*, that is, a G-equivariant birational isomorphism between the group variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley group. A linear algebraic group G is called *stably Cayley* if G x S is Cayley for some torus S. I will consider semisimple algebraic groups, in particular, simple algebraic groups. I will describe classification of Cayley simple groups and of stably Cayley semisimple groups. (Based on joint works with Boris Kunyavskii and others.)