Related papers: Finite distributive nearlattices
We represent finite join-semilattices and join-preserving morphisms as a category whose objects and morphisms are binary relations. It is a quotient category of $\mathsf{Rel}_f$'s arrow category, where self-duality arises by taking the…
A finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…
The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements…
For a finite distributive lattice $D$, let us call $Q \subseteq D$ \emph{principal congruence representable}, if there is a finite lattice $L$ such that the congruence lattice of $L$ is isomorphic to $D$ and the principal congruences of $L$…
We study Kostant's partial order on the elements of a semisimple Lie group in relations with the finite dimensional representations. In particular, we prove the converse statement of [3, Theorem 6.1] on hyperbolic elements.
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
We present a class of photonic lattices with an underlying symmetry given by a finite-dimensional representation of the 2+1D Lorentz group. In order to construct such a finite-dimensional representation of a non-compact group, we have to…
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…
A simple but elegant result of Rival states that every sublattice $L$ of a finite distributive lattice $\mathcal{P}$ can be constructed from $\mathcal{P}$ by removing a particular family $\mathcal{I}_L$ of its irreducible intervals.…
We study Dirichlet forms and Laplacians on self-similar sets with overlaps. A notion of "finitely ramified of finite type($f.r.f.t.$) nested structure" for self-similar sets is introduced. It allows us to reconstruct a class of self-similar…
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…
This paper primarily studies monomial ideals by their associated lcm-lattices. It first introduces notions of weak coordinatizations of finite atomic lattices which have weaker hypotheses than coordinatizations and shows the…
This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…
The goal of this paper is to prove that several variants of deciding whether a poset can be (weakly) embedded into a small Boolean lattice, or to a few consecutive levels of a Boolean lattice, are NP-complete, answering a question of Griggs…
The aim of this paper is to investigate further properties of $z$-elements in multiplicative lattices. We utilize $z$-closure operators to extend several properties of $z$-ideals to $z$-elements and introduce various distinguished…
We give two sufficient conditions for the lattice Co(R^n,X) of relatively convex sets of n-dimensional real space R^n to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice…
Finite fields form an important chapter in abstract algebra, and mathematics in general. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a…
We present a novel approach to the construction of new finite algebras and describe the congruence lattices of these algebras. Given a finite algebra $(B_0, \dots)$, let $B_1, B_2, \dots, B_K$ be sets that either intersect $B_0$ or…
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…