Related papers: Strongly modular lattices with long shadow
We prove that the classification problem for graphs and several types of algebraic lattices (distributive, congruence and modular) up to isomorphism contains the classification problem for pairs of matrices up to simultaneous similarity.
The classification of reflective modular forms is an important problem in the theory of automorphic forms on orthogonal groups. In this paper, we develop an approach based on the theory of Jacobi forms to give a full classification of…
A planar semimodular lattice $L$ is \emph{slim} if $\mathbf{M}_3$ is not a sublattice of $L$. In a recent paper, G. Cz\'edli introduced a very powerful diagram type for slim, planar, semimodular lattices. This short note proves the…
We characterize conjugacy classes of isometries of odd prime order in unimodular Z-lattices. This is applied to give a complete classification of odd prime order non-symplectic automorphisms of irreducible holomorphic symplectic manifolds…
We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related…
In this note we study the finite groups whose subgroup lattices are dismantlable.
We denote by Conc(L) the semilattice of all finitely generated congruences of a lattice L. For varieties (i.e., equational classes) V and W of lattices such that V is contained neither in W nor its dual, and such that every simple member of…
We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.
We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields.
In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…
In this paper we describe an algorithm for classifying orbits of vectors in Lorentzian lattices. The main point of this is that isomorphism classes of positive definite lattices in some genus often correspond to orbits of vectors in some…
For any continuous self-map of a compact metric space, we consider the space of chain components and prove that the s-limit shadowing implies the denseness of chain components with the shadowing property. It gives a partial answer to a…
Laser beams can be made to form bright and dark intensity helices of light. Such helices have a pitch length on the order of a wavelength and may have applications in lithography and the manipulation of particles through optical forces. The…
We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.
This article provides the second part of the research initiated in arXiv:2411.17381, where we introduced and investigated so called periodicity shadows, which are special skew-symmetric matrices related to symmetric algebras with periodic…
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…
It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only for even unimodular lattices. Quebbemann had extended the…
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…
Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.