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In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…

Mathematical Physics · Physics 2007-05-23 B. Schroer , H. -W. Wiesbock

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…

Mathematical Physics · Physics 2022-06-20 Evan Patterson , Andrew Baas , Timothy Hosgood , James Fairbanks

Wiring diagrams usually serve as a tool in the study of arrangements of lines and pseudolines. In this paper we go in the opposite direction, using known properties of line arrangements to motivate certain equivalence relations and actions…

Algebraic Geometry · Mathematics 2007-05-23 David Garber , Mina Teicher , Uzi Vishne

The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order modular forms, and iterated Eichler-Shimura integrals.…

Number Theory · Mathematics 2021-05-18 Michael H. Mertens , Martin Raum

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

Representation Theory · Mathematics 2007-05-23 Fernando Muro

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

Representation Theory · Mathematics 2024-11-26 Tyrone Crisp , Ehud Meir , Uri Onn

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

Mathematical Physics · Physics 2007-05-23 G. Gaeta , S. Walcher

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…

Group Theory · Mathematics 2015-02-27 James East , Attila Egri-Nagy , Andrew R. Francis , James D. Mitchell

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…

Disordered Systems and Neural Networks · Physics 2008-02-28 J. P. Bagrow , E. M. Bollt , J. D. Skufca , D. ben-Avraham

The object-oriented class is, in general, the most utilized element in programming and modeling. It is employed throughout the software development process, from early domain analysis phases to later maintenance phases. A class diagram…

Software Engineering · Computer Science 2017-10-03 Sabah Al-Fedaghi

A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…

Quantum Algebra · Mathematics 2018-10-23 Andrew Schopieray

We define pullback and separated presentations of modules over pullback rings, and, if the ring is a pullback of epimorphisms over a semisimple ring, an algorithm reducing such a presentation of a module to an $R$-diagram. The latter is the…

Commutative Algebra · Mathematics 2013-12-17 Krzysztof K. Putyra

Classical diagram categories and monoids, including the Temperley--Lieb, Brauer, and partition cases, arise as special instances of the category of two dimensional cobordisms and admit additional twists that produce a large new family of…

Representation Theory · Mathematics 2025-12-22 Matthias Fresacher , Willow Stewart , Daniel Tubbenhauer

We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…

Representation Theory · Mathematics 2021-05-17 Lucas Calixto , Tiago Macedo

A general procedure is presented which associates to a finite crossed module a premodular category, generalizing the representation categories of a finite group and of its double, and the extent to which the resulting category fails to be…

Quantum Algebra · Mathematics 2007-05-23 P. Bantay

We define a class of monoidal categories whose morphisms are diagrams, and which are enhancements and generalisations of the Brauer category obtained by adjoining infinitesimal braids, "coupons" and poles. Properties of these categories are…

Representation Theory · Mathematics 2024-04-02 Gustav Lehrer , Ruibin Zhang

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…

Rings and Algebras · Mathematics 2016-09-15 Donald W. Barnes

We introduce nominal string diagrams as, string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we…

Logic in Computer Science · Computer Science 2019-04-17 Samuel Balco , Alexander Kurz

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

Algebraic Topology · Mathematics 2016-09-28 Frederick R. Cohen , Mentor Stafa

Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal module for a finite group in the setting of holomorphic mock…

Representation Theory · Mathematics 2023-03-14 Miranda C. N. Cheng , John F. R. Duncan , Michael H. Mertens