New Automorphisms of Generic Matrix Algebras and Polynomial Algebras Original Research Article

LetTbe the generic trace algebra generated by the algebraRof two generic 2 × 2 matrices and by all traces of the matrices fromRover a fieldK. We construct new automorphisms ofTandR. They induce automorphisms of the polynomial algebra in five variables which fix two of the variables. Our automorphisms ofRare wild. We do not know if the new automorphisms ofK[x1,…,x5] are tame. When char K ≠ 2 we give the explicit form of all the constructed automorphisms.