Related papers: Automorphisms of decompositions

Given an integer $k\ge3$ and a group $G$ of odd order, if there exists a $2$-$(v,k,1)$-design and if $v$ is sufficiently large, then there is such a design whose automorphism group has a subgroup isomorphic to $G$. A weaker result is proved…

For a given extension $A \subset E$ of associative algebras we describe and classify up to an isomorphism all $A$-complements of $E$, i.e. all subalgebras $X$ of $E$ such that $E = A + X$ and $A \cap X = \{0\}$. Let $X$ be a given…

This article studies automorphism groups of graph products of arbitrary groups. We completely characterise automorphisms that preserve the set of conjugacy classes of vertex groups as those automorphisms that can be decomposed as a product…

We study the problem of topologically order-embedding a given topological poset X in the space of all closed subsets of X which is topologized by the Fell topology and ordered by set inclusion. We show that this can be achieved whenever X…

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…

Given a countable abelian group $A$, we construct a row finite directed graph $\Gamma(A)$ such that the $K_{0}$-group of the graph $\textrm{C}^{\ast}$-algebra $\textrm{C}^{\ast}(\Gamma(A))$ is canonically isomorphic to $A$. Moreover, each…

Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…

The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

Let $P$ be a compact hyperbolic Coxeter truncation polytope of dimension $d\ge 3$, and let $\Gamma$ be the orbifold fundamental group of the associated Coxeter orbifold $\mathcal{O}_P$. Let $\mathscr{G}(\Gamma,G)$ be the geometric component…

Given an automorphism of a smooth complex algebraic curve, there is an induced action on the moduli space of semi-stable rank 2 holomorphic bundles with fixed determinant. We give a complete description of the fixed variety in terms of…

Let $X$ be a product of locally compact rank one Hadamard spaces and $\Gamma$ a discrete group of isometries which contains two elements projecting to a pair of independent rank one isometries in each factor. In [arXiv:1308.5584] we gave a…

This paper deals with the extension of partial actions of topological groups on topological spaces. Within this framework, we introduce a class of topological embeddings defined via the inverse semigroup of homeomorphisms between open…

Let $f:G\rightarrow H$ be a homomorphism of groups, we construct a topological space $X_f$ such that its group of homeomorphisms is isomorphic to $G$, its group of homotopy classes of self-homotopy equivalences is isomorphic to $H$ and the…

A decomposition space (also called 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses composition, the new condition expresses decomposition. It is…

Let $X$ be a connected, compact complex manifold and $S\subset X$ a separating real hypersurface, so that $X$ decomposes as a union of compact complex manifolds with boundary $\bar X^\pm$. Let $\mathcal{M}$ be the moduli space of $S$-framed…

This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

We give density results for automorphic representations of Hilbert modular groups. In particular, we show that there are infinitely many automorphic representations that have a prescribed discrete series factor at some (but not all) real…

The lattice of intersections of reflecting hyperplanes of a complex reflection group W may be considered as the poset of 1-eigenspaces of the elements of W. In this paper we replace 1 with an arbitrary eigenvalue and study the topology and…

There is a family of constructions to produce orthomodular structures from modular lattices, lattices that are M and M*-symmetric, relation algebras, the idempotents of a ring, the direct product decompositions of a set or group or…