Compact presentability of tree almost automorphism groups

Tree actions of automorphism groups

We introduce conditions on a group action on a tree that are sufficient for the action to extend to the automorphism group. We apply this to two different classes of one-relator groups: certain BaumslagSolitar groups and one-relator groups with centre. In each case we derive results about the automorphism group, and deduce that there are relatively few outer automorphisms.

Compact automorphism groups of vertex operator algebras

Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for G and the irreducible modules for V G which are contained in V where V G is the space of G-invariants of V. We also prove a concomitant Galois correspondence between vertex operator s...

Reinhardt Domains with Non-compact Automorphism Groups

We give an explicit description of smoothly bounded Reinhardt domains with noncompact automorphism groups. In particular, this description confirms a special case of a conjecture of Greene/Krantz. 0. Introduction Let D be a bounded domain in C, n ≥ 2. Denote by Aut(D) the group of holomorphic automorphisms of D. The group Aut(D) with the topology of uniform convergence on compact subsets of D i...

Almost commuting elements in compact Lie groups

Solvable automorphism groups of a compact Kähler manifold

Let X be a compact Kähler manifold of complex dimension n, and let G be a connected solvable subgroup of the automorphism group Aut(X). Let N(G) be the normal subgroup of G of elements of null entropy. The aim of this short paper is to show that if X admits a Kähler metric invariant under G then G/N(G) is a free abelian group of rank ≤ n − 1 and that the rank estimate is optimal. This proves af...