On triangularizable polynomial automorphisms

Length Four Polynomial Automorphisms

We study the structure of length four polynomial automorphisms of R[X, Y ] when R is a UFD. The results from this study are used to prove that if SLm(R[X1, X2, . . . , Xn]) = Em(R[X1, X2, . . . , Xn]) for all n, m ≥ 0 then all length four polynomial automorphisms of R[X, Y ] that are conjugates are stably tame.

Subgroups of Polynomial Automorphisms

Throughout this paper, k will denote a commutative ring containing the rational numbers Q, and k = k[x{, . . . , xn] will be the polynomial ring over k . If ƒ : k —• k is a polynomial map (i.e., a fc-algebra homomorphism), then ƒ is a polynomial automorphism provided there is an inverse ƒ " which is also a polynomial map. Very little is known about the group of polynomial automorphisms, and ind...

ON POLYNOMIAL AUTOMORPHISMS OF AFFINE SPACESVladimir

Polynomial composition rigidity and plane polynomial automorphisms

In the first part of this paper, we briefly present a conjecture dealing with polynomial composition and we prove it in some particular cases. In the second and longest part, we prove our main result, which consists of an application of the conjecture to plane polynomial automorphisms. More precisely, we describe the closure of the set of plane polynomial automorphisms having a prescribed multi...

Equivariant Polynomial Automorphisms of -representations

We show that every equivariant polynomial automorphism of a-representation and of the reduction of an irreducible-representation is a multiple of the identity.