By a graph X we mean a finite set V(X), called the vertices of X, together with a set E(X), called the edges of X, consisting of unordered pairs of distinct elements of V(X). We shall indicate the unordered pairs by brackets. Two graphs X and Y are said to be isomorphic, denoted by X cz Y, if there is a one-to-one map a of V(X) onto V(Y) such that [aa,ab~\eE(Y) if and only if [a, b~]eE(X). An i...

§0. Introduction. Cantat [C1] has shown that if a compact projective surface carries an automorphism of positive entropy, then it has a minimal model which is either a torus, K3, or rational (or a quotient of one of these). It has seemed that rational surfaces which carry automorphisms of positive entropy are relatively rare. Indeed, the first infinite family of such rational surfaces was found...

If G is a free product of finite groups, let ΣAut1(G) denote all (necessarily symmetric) automorphisms of G that do not permute factors in the free product. We show that a McCullough-Miller [D. McCullough and A. Miller, Symmetric Automorphisms of Free Products, Mem. Amer. Math. Soc. 122 (1996), no. 582] and Gutiérrez-Krstić [M. Gutiérrez and S. Krstić, Normal forms for the group of basis-conjug...

In this paper we consider some algebraic structures associated to a class of outer automorphisms of generalized Kac-Moody (GKM) algebras. These structures have recently been introduced in [2] for a smaller class of outer automorphisms in the case of ordinary Kac-Moody algebras with symmetrizable Cartan matrices. A GKM algebra G = G(A) is essentially described by its Cartan matrix, A = (aij)i,j∈...

Bigger diagrams make visible more automorphisms: more precisely, bigger diagrams with the same limit make visible more automorphisms of the same object. In the case of the 2-solenoid, this means that we will find a copy of the 2-adic rational numbers [1] Q2 acting on the 2-solenoid, rather than merely the 2-adic integers Z2. This is a big change in the sense that Q2 is non-compact, while Z2 is ...

Many important quantum algebras such as quantum symplectic space, quantum Euclidean space, quantummatrices, q-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras U(L+) of even Lie color algebras are also semi-commutative. In this paper, we generalize work of Montgomery and examine the X-inner automorphisms of such algebras. The t...

Abstract In this paper, we introduce an AEC framework for studying fields with commuting automorphisms. Fields automorphisms are closely related to difference fields. Some authors define a ring (or field) as together several endomorphisms, while others only study one endomorphism. Z. Chatzidakis and E. Hrushovski have studied in depth the model theory of ACFA, companion automorphism. Our genera...

We bound the number of fixed points of an automorphism of a real curve in terms of the genus and the number of connected components of the real part of the curve. Using this bound, we derive some consequences concerning the maximum order of an automorphism and the maximum order of an abelian group of automorphisms of a real curve. We also bound the full group of automorphisms of a real hyperell...

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...

We bound the number of fixed points of an automorphism of a real curve in terms of the genus and the number of connected components of the real part of the curve. Using this bound, we derive some consequences concerning the maximum order of an automorphism and the maximum order of an abelian group of automorphisms of a real curve. We also bound the full group of automorphisms of a real hyperell...