Related papers: Fusion systems in representation theory

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…

This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…

We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…

We study group models for fusion systems and construct homology decompositions for the models of Robinson and Leary-Stancu type.

This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…

How best to think about quantum systems under permutation invariance is a question that has received a great deal of attention in the literature. But very little attention has been paid to taking seriously the proposal that permutation…

Fusion is a common tool for the analysis and utilization of available datasets and so an essential part of data mining and machine learning processes. However, a clear definition of the type of fusion is not always provided due to…

We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…

In recent years, unsupervised and self-supervised graph representation learning has gained popularity in the research community. However, most proposed methods are focused on homogeneous networks, whereas real-world graphs often contain…

We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. We establish a relationship between the characteristic…

Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…

Linking systems were introduced to provide algebraic models for $p$-completed classifying spaces of fusion systems. Every linking system over a saturated fusion system $\mathcal{F}$ corresponds to a group-like structure called a locality.…

In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and…

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…

A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…

We outline the basic questions that are being studied in the theory of entanglement. Following a brief review of some of the main achievements of entanglement theory for finite-dimensional quantum systems such as qubits, we will consider…

The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…