On Linear Representations of Some Extensions

Details On Linear Representations of Some Extensions On Linear Representations of Some Extensions

2005-06-07

arxiv.org/abs/math/0506114v3

Mathematics

Group Theory

15 pages

Scientific paper

Yu. I. Merzljakov developed a method of splittable coordinates which helps to verify the linearity of some groups, he established some fundamental results using this method. In this paper we use the method of splittable coordinates and find some sufficient condition under which the semi--direct product of two linear groups is linear. As consequence we get linearity of some HNN-extensions of a free group, linearity of the holomorph of the braid group B_n, n >1, and linearity of some Artin groups. In all cases we construct faithful linear representations in the explicit form.

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