Problems for Problem Session

is its closed normal subgroup, [Sh], [Ka]. The group Aut∗k k [n] is an infinite dimensional simple algebraic group, [Sh]. If D is a locally nilpotent k-derivation of k, then it is easily seen that exp tD ∈ Aut∗k k [n] for any t ∈ k, so D lies in Lie(Aut∗k k ). It follows from [BB1], [BB2] that n − 1 is the maximum of dimensions of algebraic tori contained in Aut∗k k , and that every algebraic torus in Aut∗k k [n] of dimension n− 1 is conjugate to the ‘diagonal’ torus