Related papers: Domain Range Semigroups and Finite Representations
Domain operations on semirings have been axiomatised in two different ways: by a map from an additively idempotent semiring into a boolean subalgebra of the semiring bounded by the additive and multiplicative unit of the semiring, or by an…
We represent finite join-semilattices and join-preserving morphisms as a category whose objects and morphisms are binary relations. It is a quotient category of $\mathsf{Rel}_f$'s arrow category, where self-duality arises by taking the…
In this short note we show that every connected reductive simply-connected algebraic group of rank $>1$ over the complex numbers has infinitely many pairs of irreducible representations which are not related by an automorphism of the…
In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary. The atom structures of such algebras are cylindric…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite…
We consider the following question, concerning associative algebras R over an algebraically closed field k: When can the space of (equivalence classes of) finite dimensional irreducible representations of R be topologically embedded into a…
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…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…
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…
Let $K$ be a commutative Noetherian ring with identity, let $A$ be a $K$-algebra, and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…
We classify the finite dimensional semi-weight representations of the reduced stated skein algebras at odd roots of unity of connected marked surfaces which either have a boundary component with at least two boundary edges or which do not…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…
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.
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We consider the proportion of zero entries in the character table of a sequence of reductive groups over a finite field. We prove an asymptotic lower bound when the reductive group is fixed and the size of the finite field increases.…
We deal with equations over free semilattice of infinite rank and prove that any infinite consistent system of equations is equivalent to its finite subsystem. Moreover, we describe irreducible algebraic sets and solve some algorithmic…