Related papers: Coset relation algebras

The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…

Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…

Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the…

We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure $M$. We prove that if $T$ is a complete $L$-theory, then $T$ is mutually algebraic if and only if there is some model $M$ of $T$ for…

We study macroscopic observables defined as the total value of a physical quantity over a collection of quantum systems. We show that previous results obtained for infinite ensemble of identically prepared systems lead to incorrect…

In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in…

The poset of copies of a relational structure ${\mathbb X}$ is the partial order ${\mathbb P} ({\mathbb X} ) := \langle \{ Y \subset X: {\mathbb Y} \cong {\mathbb X}\}, \subset \rangle$ and each similarity of such posets (e.g. isomorphism,…

A measure-scaling quasi-isometry between two connected graphs is a quasi-isometry that is quasi-$\kappa$-to-one in a natural sense for some $\kappa>0$. For non-amenable graphs, all quasi-isometries are quasi-$\kappa$-to-one for any…

For a C*-algebra A, G. Pedersen defined the concept of universal measurability for self-adjoint elements of A**, the universal enveloping algebra of A. Although he was unable to show that U, the set of universally measurable elements, is a…

This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…

Metric algebras are metric variants of $\Sigma$-algebras. They are first introduced in the field of universal algebra to deal with algebras equipped with metric structures such as normed vector spaces. Recently a similar notion of…

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero…

In a convolution semigroup over a locally compact group, measurability of the translation by a fixed element implies continuity. In other words, the measurable centre coincides with the topological centre.

Let $S_\infty$ denote the topological group of permutations of the natural numbers. We study the complexity of the isomorphism relation on classes of closed subgroups $S_\infty$ in the setting of Borel reducibility between equivalence…

In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…

Exactly solvable models of linear aggregation have been known since Ising's seminal one-dimensional model. This model is defined by a unique nearest-neighbour bond strength that is independent of the length of the cluster; known as…

Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…

In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary. The atom structures of such algebras are cylindric…