Related papers: On some admissible lattices
Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the…
Let K be a number field, let A be a finite dimensional semisimple K-algebra and let Lambda be an O_K-order in A. It was shown in previous work that, under certain hypotheses on A, there exists an algorithm that for a given (left)…
The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
We present a general formalism to investigate the integrable properties of a large class of non-ultralocal models which in principle allows the construction of the corresponding lattice versions. Our main motivation comes from the su(1|1)…
The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of…
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…
Recently there has been significant progress in classifying integer friezes and $\text{SL}_2$-tilings. Typically, combinatorial methods are employed, involving triangulations of regions and inventive counting techniques. Here we develop a…
Slim semimodular lattices were introduced by G. Gr\"atzer and E. Knapp in 2007, and they have intensively been studied since then. It is often reasonable to give these lattices by their $\mathcal C_1$-diagrams defined by the author in 2017.…
The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…
In a previous paper {GN2} an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean ergodic theorem for the…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
This article is part of my upcoming masters thesis which investigates the following open problem from the book, Free Lattices, by R.Freese, J.Jezek, and J.B. Nation published in 1995: "Which lattices (and in particular which countable…
The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed…
Introduction of a twist between layers of two-dimensional materials which leads to the formation of a moir\'e pattern is an emerging pathway to tune the electronic, vibrational and optical properties. The fascinating properties of these…
In the literature on Kleene algebra (KA), a number of variants have been proposed such as Kleene algebra with tests, commutative KA, bi-KA, and concurrent KA. The equational theories of some of these structures have then been studied in the…
We study the Hobby-McKenzie varieties that constitute a major class investigated thoroughly in the monograph The shape of congruence lattices by Kearnes and Kiss. We obtain new characterizations of the Hobby-McKenzie varieties via…
Let $L$ be a planar semimodular lattice. We call $L$ \emph{slim}, if it has no $\mthree$ sublattice. Let us define an \emph{SPS lattice} as a slim, planar, semimodular lattice $L$. In 2016, I proved a property of congruences of SPS lattices…
In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted…