New automorphisms of generic matrix algebras and polynomial algebras

Let T be the generic trace algebra generated by the algebra R of two generic 2 x 2 matrices and by all traces of the matrices from R over a field K. We construct new automorphisms of T and R. They induce automorphisms of the polynomial algebra in five variables which fuc tio of the variables. Our automorphisms of R are wild. We do not know if the new automorphisms of K[x(1),...,x(5)] are tame. When char K not equal 2 we give the explicit form of all the constructed automorphisms. (C) 1997 Academic Press.