Related papers: The Reverse Representation Problem

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 structure of a certain subgroup $S$ of the automorphism group of a partially commutative group (RAAG) $G$ is described in detail: namely the subgroup generated by inversions and elementary transvections. We define admissible subsets of…

Let $S$ be a set of transpositions such that the girth of the transposition graph of $S$ is at least 5. It is shown that the automorphism group of the Cayley graph of the permutation group $H$ generated by $S$ is the semidirect product…

For each subchain $X'$ of a chain $X$, let $T_{RE}(X, X')$ denote the semigroup under composition of all full regressive transformations, $\alpha:X\rightarrow X'$ satisfying $x\alpha\leq x$ for all $x\in X$. Necessary and sufficient…

We prove a version of Wordingham's theorem for left regular representations in the setting of Fell bundles of inverse semigroups and use this result to discuss the various associated cross sectional C*-algebras.

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

Let $T(X)$ (resp. L(V)) be the semigroup of all transformations (resp. linear transformations) of a set $X$ (resp. vector space $V$). For a subset $Y$ of $X$ and a subsemigroup $\mathbb{S}(Y)$ of $T(Y)$, consider the subsemigroup…

Let $\mathcal P(S)$ be the semigroup obtained by equipping the family of all non-empty subsets of a (multiplicatively written) semigroup $S$ with the operation of setwise multiplication induced by $S$ itself. We call a subsemigroup $P$ of…

This paper introduces a notion of presentation for locally inverse semigroups and develops a graph structure to describe the elements of locally inverse semigroups given by these presentations. These graphs will have a role similar to the…

We show that groups presented by inverse-closed finite convergent length-reducing rewriting systems are characterised by a striking geometric property: their Cayley graphs are geodetic and side-lengths of non-degenerate triangles are…

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement…

A linear algebraic group G is over a field K is called a Cayley K-group if it admits a Cayley map, i.e., a G-equivariant K-birational isomorphism between the group variety G and its Lie algebra. We classify real reductive algebraic groups…

In this paper, we describe a regular representation given by Cayley theorem for 2-crossed modules of groups and their associated Gray 3-group groupoids with a single 0-cell and equivalently cat2-groups.

We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in…

Each infinitesimally faithful representation of a reductive complex connected algebraic group $G$ induces a dominant morphism $\Phi$ from the group to its Lie algebra $\g$ by orthogonal projection in the endomorphism ring of the…

The current form of quantum mechanics is very successful and is almost certainly correct. It is remarkable, however, that the entire structure-from the mass, spin and charge labels on particlelike states to antisymmetry to broken internal…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

In this paper we formulate and study the problem of representing groups on graphs. We show that with respect to polynomial time turing reducibility, both abelian and solvable group representability are all equivalent to graph isomorphism,…

We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by…

We prove the existence of a regular semigroup F(X) weakly generated by X such that all other regular semigroups weakly generated by X are homomorphic images of F(X). The semigroup F(X) is introduced by a presentation and the word problem…