Related papers: Toeplitz subshift whose automorphism group is not …

We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual one. We…

It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $\mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the…

The automorphism tower of a group is obtained by computing its automorphism group, the automorphism group of THAT group and so on, iterating transfinitely. Each group maps into the next using inner automorphisms and one takes a direct limit…

For a real, non-singular, 2-step nilpotent Lie algebra $\mathfrak{n}$, the group \Aut(\mathfrak{n})/\Aut_0(\mathfrak{n})$, where $\Aut_0(\mathfrak{n})$ is the group of automorphisms which act trivially on the center, is the direct product…

The Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. For…

We show that there is a distortion element in a finitely-generated subgroup $G$ of the automorphism group of the full shift, namely an element of infinite order whose word norm grows polylogarithmically. As a corollary, we obtain a lower…

In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…

We study the stabilized automorphism group of minimal and, more generally, certain transitive dynamical systems. Our approach involves developing new algebraic tools to extract information about the rational eigenvalues of these systems…

We classify the pairs $(X,\pi)$, where $\pi\colon X\to S$ is a $\mathbb{P}^1$-bundle over a non-rational geometrically ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the…

We give a new computer-assisted proof of the classification of maximal subgroups of the simple group ${}^2E_6(2)$ and its extensions by any subgroup of the outer automorphism group $S_3$. This is not a new result, but no earlier proof…

We show that the automorphism group of a certain subclass of smooth Gizatullin surfaces with a distinguished and rigid extended divisor is generated by automorphisms of A1-fibrations. Moreover, such surfaces provide examples of smooth…

This paper studies two-variable compressions of shifts associated to rational inner functions on the bidisk; these generalize the classical compressions of the shift associated to finite Blasckhe products and are unitarily equivalent to…

This article deals with inductive systems of Toeplitz algebras over arbitrary directed sets. For such a system the family of its connecting injective $*$-homomorphisms is defined by a set of natural numbers satisfying a factorization…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent monograph 'Strongly regular graphs' by Brouwer and Van…

We describe an underlying right angled building structure of any graph product of buildings. We describe the automorphism group of the graph product of buildings. We show that the notion of generalized graph product of a collection of…

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…

A subperiodic group is a group of motions of $d$-dimensional Euclidean space $\R^d$ which contains a translation lattice $\Z^r$ of rank $r < d$ as a subgroup of finite index. A classification into abstract group isomorphism classes is…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

For convex domains with $C^{1,\epsilon}$ boundary we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different closed complex faces of the boundary, then the…