REPRESENTATIONS OF ARTIN BRAID-GROUPS

The purpose of this Note is to describe a method of constructing families of representations of the Artin braid groups B-n. The main tool used is a sequence of algebras H-n with coefficients in a non-commutative ring. These algebras are studied; some of their factors ave determined. We prove that the new algebra H-n is a non-trivial extension of the classical Hecke algebra H-n. Explicit matrix representations of braid groups are obtained.