Group Gₙ³ and imaginary generators

الأصل · EN

In the present paper, we construct a monomorphism from (Artin) pure braid group PBₙ into a group, which is `bigger' than PBₙ. Roughly speaking, this mapping is defined on words of braids by adding `new generators' between generators of PBₙ. 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 PBₙ and the minimality can be shown by the invariant.