Related papers: A lecture note on covering theory in representatio…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb…
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…
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of $Q$-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
The aim of this paper is to give new representation theorems for extended contact algebras. These representation theorems are based on equivalence relations.
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
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…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
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…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is…
We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…
A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…
These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required…