A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group Bn . In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from th...

Every affine structure on Lie algebra g defines a representation of g in aff(Rn). If g is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra. 200...

For a finite group G, we denote by μ(G) and c(G), the minimal degree of faithful permutation representation G quasi-permutation matrices over complex field C respectively. In this paper, examine c(G) for VZ-groups Camina p-groups.

Abstract The Dowker complex is an abstract simplicial that constructed from a binary relation in straightforward way. Although there are two ways to perform this construction—vertices for the either rows or columns of matrix representing relation—the constructions homotopy equivalent. This article shows construction non-faithful covariant functor. Furthermore, we show functor can be made faithf...

The aim of this short note is to answer a question by Guoliang Yu of whether the group EL3(Z〈x, y〉), where Z〈x, y〉 is the free (non-commutative) ring, has any faithful finite dimensional linear representations over a field. Recall that for every (associative unitary) ring R the group ELn(R) is the subgroup of GLn(R) generated by all n × n-elementary matrices xij(r) = Id + reij (r ∈ R, 1 ≤ i 6= ...

the freiheitssatz of magnus for one-relator groups is one of the cornerstones of combinatorial group theory. in this short note which is mostly expository we discuss the relationship between the freiheitssatz and corre-sponding results in free power series rings over fields. these are related to results of schneerson not readily available in english. this relationship uses a faithful representa...

Zhedanov’s algebra AW (3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey–Wilson polynomials. It is proved that this representation is faithful for a certain quotient of AW (3) such that the Casimir operator is equal to a special constant. Some explicit aspects of the double ...

4. Proof of Theorem 2. Harish-Chandra [l] and others have proved that every Lie algebra over a field of characteristic zero has a faithful representation. Consequently by Lemma 4, 8 has a faithful representation x—*Qx whose matrices have elements in an algebraic extension $ of g such that t(QxQv) =0 for all x of 31 and all y of 8. We now apply another form of Cartan's criterion for solvability ...

In the paper, we study finitely generated linear groups of finite rank which have faithful irreducible primitive representations over a field characteristic zero. We prove that if an infinite group [Formula: see text] has representation zero then text]-center is infinite.