Related papers: A classification of Curtis-Tits amalgams

This paper deals with finite cubic ($3$-regular) graphs whose automorphism group acts transitively on the edges of the graph. Such graphs split into two broad classes, namely arc-transitive and semisymmetric cubic graphs, and then these…

Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver Q is a C*-correspondence, and from this correspondence one may…

We study the arithmetic of Galois-invariant sets of points on algebraic curves with controlled reduction behavior. Let $C$ be a smooth projective curve with a smooth proper model $\mathcal{C}$ over $\mathcal{O}_{K,S}$. We define $\Omega_n$…

We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…

We study rational curves on smooth complex Calabi--Yau threefolds via noncommutative algebra. By the general theory of derived noncommutative deformations due to Efimov, Lunts and Orlov, the structure sheaf of a rational curve in a smooth…

A group $G$ splits over a subgroup $C$ if $G$ is either a free product with amalgamation $A \underset{C}{\ast} B$ or an HNN-extension $G=A \underset{C}{\ast} (t)$. We invoke Bass-Serre theory and classify all infinite groups which admit…

We prove a purely topological characterization of the Moufang property for disconnected compact polygons in terms of convergence groups. As a consequence, we recover the fact that a locally finite thick affine building of rank 3 is a…

Given a locally finite leafless tree $ T $, various algebraic groups over local fields might appear as closed subgroups of $ \text{Aut} (T)$. We show that the set of closed cocompact subgroups of $ \text{Aut} (T)$ that are isomorphic to a…

Given two automorphisms of a group $G$, one is interested in knowing whether they are conjugate in the automorphism group of $G$, or in the abstract commensurator of $G$, and how these two properties may differ. When $G$ is the fundamental…

A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…

We apply the Fixed Point Theorem for the actions of finite groups on Bruhat-Tits buildings and their products to establish two results concerning the groups of points of reductive algebraic groups over polynomial rings in one variable,…

The so-called Tits class, associated to an adjoint absolutely almost simple algebraic group, provides a cohomological obstruction for this group to admit an outer automorphism. If the group has inner type, this obstruction is the only one.…

For a finite group $G$, we define the inclusion graph of subgroups of $G$, denoted by $\mathcal I(G)$, is a graph having all the proper subgroups of $G$ as its vertices and two distinct vertices $H$ and $K$ in $\mathcal I(G)$ are adjacent…

Building on a construction of J-P. Serre, we associate to any graph of C*-algebras a maximal and a reduced fundamental C*-algebra and use this theory to construct the fundamental quantum group of a graph of discrete quantum groups. This…

Let $G=G_1\ast\dots\ast G_k\ast F$ be a countable group which splits as a free product, where all groups $G_i$ are freely indecomposable and not isomorphic to $\mathbb{Z}$, and $F$ is a finitely generated free group. If for all…

For a finite group $G$, the vertices of the prime graph $\Gamma(G)$ are the primes that divide $|G|$, and two vertices $p$ and $q$ are connected by an edge if and only if there is an element of order $pq$ in $G$. Prime graphs of solvable…

The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…

The present paper, which is partially a review, but also contains several completely new results, aims at presenting, in a unified mathematical framework, a complex and articulated lore regarding non-compact symmetric spaces, with negative…

The configuration space $\mathcal{C}^n(X)$ of an algebraic curve $X$ is the algebraic variety consisting of all $n$-point subsets $Q\subset X$. We describe the automorphisms of $\mathcal{C}^n(\mathbb{C})$, deduce that the (infinite…

Triangles of groups have been introduced by Gersten and Stallings. They are, roughly speaking, a generalisation of the amalgamated free product of two groups and occur in the framework of Corson diagrams. First, we prove an intersection…