Let π1 be the fundamental group of a closed surface Σ of genus g > 1. One of the fundamental problems in complex hyperbolic geometry is to find all discrete, faithful, geometrically finite and purely loxodromic representations of π1 into SU(2, 1), (the triple cover of) the group of holomorphic isometries of H2C. In particular, given a discrete, faithful, geometrically finite and purely loxodrom...

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible size. We study the structure of such representations and show that for certain groups they may be obtained by a greedy construction. In these situations (except when central involutions intervene) all minimal permutation representations have the same set of orbit sizes. Using the same ideas w...

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible cardinality. We study the structure of such representations and show that for most groups they may be obtained by a greedy construction. It follows that whenever the algorithm works (except when central involutions intervene) all minimal permutation representations have the same set of orbit ...

The purpose of this article is to record the center of the Lie algebra obtained from the descending central series of Artin’s pure braid group, a Lie algebra analyzed in work of Kohno [12, 13, 14], and Falk-Randell [9]. The structure of this center gives a Lie algebraic criterion for testing whether a homomorphism out of the classical pure braid group is faithful which is analogous to a criteri...

The free lattice-ordered group Fn (of rank r¡) has been studied in two ways: via the Conrad representation on the various right orderings of the free group Gv (sharpened by Kopytov's observation that some one right ordering must by itself give a faithful representation), and via the Glass-McCleary representation as a pathologically o-2-transitive /-permutation group. Each kind of representation...

This article focuses on the role loyalty played in relationship between rulers and their subjects earliest Central European chronicles, written at beginning of twelfth century: Gesta principum Polonorum by Gallus Anonymous, Chronica Boemorum Cosmas Prague, twelfth-century historiographical tradition Hungarian Royal court, which survived as a part fourteenth-century century compilation called Th...

Central to a coherent understanding of cellular biology is a faithful representation of biochemical processes as it pertains to its molecular participants. Current representations underspecify our knowledge because they fail to indicate the roles of the molecular components during relevant processes. Here, we describe a knowledge representation using OWL2 that overcomes previous limitations in ...

These CSG notes contain a condensed account of a talk by V. Nikulin in the London algebra Colloquium on 24 May 2001. None of the content is original to me: it is provided simply as a service for those who missed Nikulin’s talks. I have relied mainly on my notes from the lectures, So any errors are the product of the note-taking and are not to be attributed to the content of the lectures. 1 The ...

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...