Related papers: Finite representations for two small relation alge…
In this paper we consider finite 2-groups with odd number of real conjugacy classes. On one hand we show that if $k$ is an odd natural number less than 24, then there are only finitely many finite 2-groups with exactly $k$ real conjugacy…
We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…
We construct representations of the enveloping algebra $U_q osp(2,2)$ in terms of finite difference operators and we discuss this result in the framework of quasi-exactly-solvable equations.
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.
We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.
Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition $S+T=\makeset{m+n}{m \in S, \: n \in T}$ and…
We determine derived representation type of complete finitely generated local and two-point algebras over an algebraically closed field.
We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
For representation by partial functions in the signature with intersection, composition and antidomain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only…
We extend the family of classical Schur algebras in type A, which determine the polynomial representation theory of general linear groups over an infinite field, to a larger family, the rational Schur algebras, which determine the rational…
We classify the representation type of the descent algebras of type $\A$ in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
For monomial special multiserial algebras, which in general are of wild representation type, we construct radical embeddings into algebras of finite representation type. As a consequence, we show that the representation dimension of…
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…