Related papers: Automorphism Groups of Hyperbolic Lattices
A metacyclic group $H$ can be presented as $\langle \alpha,\beta\mid \alpha^{n}=1, \ \beta^{m}=\alpha^{t}, \ \beta\alpha\beta^{-1}=\alpha^{r}\rangle$ for some $n,m,t,r$. Each endomorphism $\sigma$ of $H$ is determined by…
We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.
Polytopes are ubiquitous in different areas of mathematics. Gleason and Hubard established a factorisation theorem, stating that every abstract polytope has a unique factorisation into prime polytopes. We compute the automorphism group of a…
We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…
Group action on an algebraic structure gives a representation of the group by automorphisms on the structure. An action of a group on a lattice gives a group lattice. K.S.S. Nambooripad introduced G-lattice in 1990. In this paper revisits…
Given a group $G$ of automorphisms of a matroid $M$, we describe the representations of $G$ on the homology of the independence complex of the dual matroid $M^*$. These representations are related with the homology of the lattice of flats…
Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of 2D hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-particle…
Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…
We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity…
In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. In this sequence of papers we study the…
Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms…
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. In this sequence of papers we study the…
In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. While doing so, we describe fundamental results on hyperbolic…
Let $F(x, y)$ be a binary form of degree at least three and non-zero discriminant. In this article we compute the automorphism group $\operatorname{Aut} F$ for four families of binary forms. The first two families that we are interested in…
A new result of G. Cz\'edli states that for an ordered set $P$ with at least two elements and a group $G$, there exists a bounded lattice $L$ such that the ordered set of principal congruences of $L$ is isomorphic to $P$ and the…
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear…
We show how the exceptional isogenies of classical groups to orthogonal groups of quadratic spaces of dimensions up to 8 over fields of characteristic different from 2 may be obtained by explicit algebraic constructions using the…
In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will mainly concentrate on the groups where some elements are…
We compute Coxeter diagrams of several ``large'' reflective even 2-elementary hyperbolic lattices and their maximal parabolic subdiagrams, and give some applications of these results to the theory of K3 surfaces and hyperkahler varieties.