Group G_{n}^{3} and imaginary generators

Abstract

In the present paper, we construct a monomorphism from (Artin) pure braid group P Bn into a group, which is 'bigger' than P Bn. Roughly speaking, this mapping is defined on words of braids by adding 'new generators' between generators of P Bn. By this mapping we can get a new invariant for classical braids. As one of application of this invariant, we will show examples, which are minimal words in P Bn and the minimality can be shown by the invariant.