Related papers: Representation Theory of Finite Groups
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
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…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes. This book provides the first presentation of the…
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
We define the character of a group representation in a 2-category C. For linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory defined on pairs of commuting elements of the group. We discuss some examples and prove a…
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…
We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…
The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear…
We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.
Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension $\G$ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
This work analyses main features that should be present in knowledge representation. It suggests a model for representation and a way to implement this model in software. Representation takes care of both low-level sensor information and…
We continue the study of glider representations of finite groups $G$ with given structure chain of subgroups $e \subset G_1 \subset \ldots \subset G_d = G$. We give a characterization of irreducible gliders of essential length $e \leq d$…
The main results in this thesis deal with the representation growth of certain classes of groups. In chapter $1$ we present the required preliminary theory. In chapter $2$ we introduce the Congruence Subgroup Problem for an algebraic group…