Related papers: Two Galois connections for left quasigroups
We study different notions of quasiconvexity for a subgroup $H$ of a relatively hyperbolic group $G.$ The first result establishes equivalent conditions for $H$ to be relatively quasiconvex. As a corollary we obtain that the relative…
Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.
The right near-domain is defined to loosen near-domain axioms. Correspondence of a class of the right near-domains and a class of sharply 2--transitive groups is constructed.
We are motivated by the question that for which class of right-angled Artin groups (RAAG's), the quasi-isometry classification coincides with commensurability classification. This is previously known for RAAG's with finite outer…
Many different programs are the implementation of the same algorithm. The collection of programs can be partitioned into different classes corresponding to the algorithms they implement. This makes the collection of algorithms a quotient of…
Let p be an odd prime. The lattice of all normal subgroups and the terms of the lower and upper central series are determined for all metabelian p-groups with generator rank d=2 having abelianization of type (p,p) and minimal defect of…
We discuss certain structural analogies between supersymmetric quiver gauge theories and lattice models leading to fracton phases of matter. In particular, classes of quiver models can be viewed as lattice models having sub-system…
Let $ G $ be a connected reductive algebraic group over $ \mathbb{R} $, and $ H $ its symmetric subgroup. For parabolic subgroups $ P_{G} \subset G $ and $ P_{H} \subset H $, the product of flag varieties $ \mathfrak{X} = H/P_H \times G/P_G…
The model with the fermions coupled in the non - minimal way to the gauge theory of Lorentz group is considered. The lattice regularization is suggested. It is argued that this model may exist in the phase with broken chiral symmetry and…
This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…
A group $G$ with conjugation operation is a rack. We call such racks \emph{group racks}. In this paper we study finite group racks via their subrack lattices. Heckenberger, Shareshian, and Welker proved that the isomorphism type of the…
We introduce the concept of a quasiresiduated lattice and prove that every lattice effect algebra can be organized into a commutative quasiresiduated lattice with divisibility. Also conversely, every such a lattice can be converted into a…
We investigate ground states of $s$=1/2 Heisenberg antiferromagnets on the eleven two-dimensional (2D) Archimedian lattices by using the coupled cluster method. Magnetic interactions and quantum fluctuations play against each other subtly…
We show that the transition laws for a 2-connection can be recovered by discretizing the base 2-space of a 2-bundle into an Euclidean hypercubic lattice. The aim of this work is to serve as an example of how important results in higher…
Inspired from research subjects in sub-riemannian geometry and metric geometry, we propose uniform idempotent right quasigroups and emergent algebras as an alternative to differentiable algebras. Idempotent right quasigroups (irqs) are…
We introduce an algebraic structure we call semiquandles whose axioms are derived from flat Reidemeister moves. Finite semiquandles have associated counting invariants and enhanced invariants defined for flat virtual knots and links. We…
Sachs showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as…
We use the structure lattice, introduced in Part I, to undertake a systematic study of the class $\mathscr S$ consisting of compactly generated, topologically simple, totally disconnected locally compact groups that are non-discrete. Given…
According to a 2002 theorem by Cardaliaguet and Tahraoui, an isotropic, compact and connected subset of the group $\operatorname{GL}^+(2)$ of invertible $2\times2-\,$matrices is rank-one convex if and only if it is polyconvex. In a 2005…
A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…