Automorphisms of polynomial and power series rings

Automorphisms of Perfect Power Series Rings

Let R be a perfect ring of characteristic p. We show that the group of continuous R-linear automorphisms of the perfect power series ring over R is generated by the automorphisms of the ordinary power series ring together with Frobenius; this answers a question of Jared Weinstein.

Automorphisms of Formal Power Series Rings over a Valuation Ring

The aim of this paper is to report on recent work on liftings of groups of au-tomorphisms of a formal power series ring over a eld k of characteristic p to characteristic 0, where they are realised as groups of automorphisms of a formal power series ring over a suitable valuation ring R dominating the Witt vectors W(k): We show that the lifting requirement for a group of automorphisms places se...

Group Actions on Polynomial and Power Series Rings

Automorphisms of Polynomial Algebras and Dirichlet Series

Let Fq[x, y] be the polynomial algebra in two variables over the finite field Fq with q elements. We give an exact formula and the asymptotics for the number pn of automorphisms (f, g) of Fq[x, y] such that max{deg(f), deg(g)} = n. We describe also the Dirichlet series generating function p(s) = ∑

Reversible Skew Laurent Polynomial Rings and Deformations of Poisson Automorphisms

A skew Laurent polynomial ring S = R[x;α] is reversible if it has a reversing automorphism, that is, an automorphism θ of period 2 that transposes x and x and restricts to an automorphism γ of R with γ = γ. We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent...