Based on a normal form for braid group elements suggested by Dehornoy, we prove several representations of braid groups by automorphisms of a free group to be faithful. This includes a simple proof of the standard Artin's representation being faithful.

A band is a semigroup consisting of idempotents. It is proved that for any field K and any band S with finitely many components, the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative K-algebra. The proof of a theorem of Malcev [4, Theorem 10] on embeddability of algebras into matrix algebras over a field is corrected and it is proved that if S = F ∪ E is a b...

1 Unité de Recherche Signaux et Systémes (U2S), Ecole Supérieure de la Statistique et de l’Analyse de l’Information (ESSAI), Ecole Nationale d’Ingénieurs de Tunis (ENIT), 6 Rue des Métiers, Charguia II 2035, Tunis Carthage, Ariana, Tunis 1002, Tunisia 2 Department of Statistics, Department of Environmental Earth System Science, Woods Institute for the Environment, Stanford University, Standford...

CSP++ is a tool that makes specifications written in CSPm executable and extensible. It is the basis for a technique called selective formalism, which allows part of a system to be designed in verifiable CSPm statements, automatically translated into C++, and linked with functions coded in C++. This paper describes in detail the subset of CSPm that can be accurately translated by CSP++, and how...

We show the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the PSL2(K) representation variety, where K = C or R, answering a question of W. Goldman. We also prove the existence of faithful representations into PU(2, 1) with certain nonintegral Toledo invariants.

In this paper we consider the problem of embedding the input and hypotheses of boolean function classes in other classes, such that the natural metric structure of the two spaces is approximately preserved. We rst prove some general properties of such embedding and then suggest and discuss possible approximate embedding in the class of \half-spaces" (single layer perceptrons) with dimension pol...

The Burau representation is a natural action of the braid group Bn on the free Z[t; t−1]{module of rank n−1. It is a longstanding open problem to determine for which values of n this representation is faithful. It is known to be faithful for n = 3. Moody has shown that it is not faithful for n 9 and Long and Paton improved on Moody’s techniques to bring this down to n 6. Their construction uses...

In this paper we study some results on Noetherian semigroups. We  show that if  $S_S$ is an  strongly  faithful $S$-act and $S$ is a duo weakly Noetherian, then we have the following.

In this article we study the space of leftand bi-invariant orderings on a torsion-free nilpotent group G. We will show that generally the set of such orderings is equipped with a faithful action of the automorphism group of G. We prove a result which allows us to establish the same conclusion when G is assumed to be merely residually torsion-free nilpotent. In particular, we obtain faithful act...