Related papers: A Module-theoretic Introduction to Abstract Elemen…
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
In this paper, we introduce and investigate \emph{semicorings} over associative semirings and their categories of \emph{semicomodules.} Our results generalize old and recent results on corings over rings and their categories of comodules.…
The article is developing homological algebra in modules over non-unital rings and algebras. The main application is the definition and study of (directed) homology of $(\infty,1)$-categories and of directed spaces, including relative…
The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…
We continue the theory of $\tT$-systems from the work of the second author, describing both ground systems and module systems over a ground system (paralleling the theory of modules over an algebra). The theory, summarized categorically at…
We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\omega_1,\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language…
Autonomous driving is not one single technology but rather a complex system integrating many technologies, which means that teaching autonomous driving is a challenging task. Indeed, most existing autonomous driving classes focus on one of…
This paper explores the concept of \textbf{co-first modules}, a generalization of coprime modules, through the lens of preradicals in module theory. Building on foundational notions such as second modules and coprime modules, we introduce…
In this article, we study module categries of simple current extensions of vertex operator algebras. Under certain assumptions, we show that every module for a rational vertex operator algebra be lifted to a twisted module for an extended…
A class of Emergent Universe (EU) model is studied in the light of recent observational data. Significant constraints on model parameters are obtained from the observational data. Density parameter for a class of model is evaluated. Some of…
In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…
This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
Recently, many authors have embraced the study of certain properties of modules such as projectivity, injectivity and flatness from an alternative point of view. Rather than saying a module has a certain property or not, each module is…
Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
Recently, several authors have adopted new alternative approaches in the study of some classical notions of modules. Among them, we find the notion of subprojectivity which was introduced to measure in a way the degree of projectivity of…