Related papers: The pseudocomplementedness of modular lattices des…
We give a classification of integral lattices with virtually abelian symmetry group. As a consequence, we complete the classification of K3 surfaces with virtually abelian automorphism group. In the appendix we formulate an algorithm for…
We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices,…
We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The "compact-like" properties we consider include (local) compactness, (local)…
The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…
We consider abelian length categories, a generalization of module categories over Artin algebras. Let $\mathcal{A}$ be an abelian length category of colocal type. We show that the lattice $\mathsf{S}(\mathcal{A})$ of full additive subobject…
Besides the oscillator group, there is another four-dimensional non-abelian solvable Lie group that admits a bi-invariant pseudo-Riemannian metric. It is called split oscillator group (sometimes also hyperbolic oscillator group or Boidol's…
We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices,…
We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by B\"ottcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two…
In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…
Let $G$ be a real centre-free semisimple Lie group without compact factors. I prove that irreducible lattices in $G$ are rigid under two types of sublinear distortions. The first result is that the class of lattices in groups that do not…
A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally…
In this paper, we continue with the results in \cite{Pg} and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member…
This paper is the first part of a study devoted to description of modular elements in the lattices of semigroup and epigroup varieties. We provide strengthened necessary and sufficient conditions under which a semigroup or epigroup variety…
We initiate an investigation of lattices in a new class of locally compact groups, so called locally pro-$p$-complete Kac-Moody groups. We discover that in rank 2 their cocompact lattices are particularly well-behaved: under mild…
Given a lattice $\Lambda$ in a locally compact abelian group $G$ and a measurable subset $\Omega$ with finite and positive measure, then the set of characters associated to the dual lattice form a frame for $L^2(\Omega)$ if and only if the…
We study the existence of lattices in almost abelian Lie groups that admit left invariant locally conformal K\"ahler or locally conformal symplectic structures in order to obtain compact solvmanifolds equipped with these geometric…
Is every locally compact abelian group which admits a symplectic self-duality isomorphic to the product of a locally compact abelian group and its Pontryagin dual? Several sufficient conditions, covering all the typical applications are…
We characterize those semilattices that give rise to Boolean spaces on their associated spaces of ultrafilters. The class of 0-disjunctive semilattices, important in the theory of congruence-free inverse semigroups, plays a distinguished…
A subgroup $H$ of a topological abelian group $X$ is said to be characterized by a sequence $\mathbf v =(v_n)$ of characters of $X$ if $H=\{x\in X:v_n(x)\to 0\ \text{in}\ \mathbb T\}$. We study the basic properties of characterized…
We consider the question: When do two finite abelian groups have isomorphic lattices of characteristic subgroups? An explicit description of the characteristic subgroups of such groups enables us to give a complete answer to this question…