Linear representations of groups with translation invariant defining relationships. Some new series of braid group representations and new invariants of links and knots

In this paper we indicate one method of construction of linear representations of groups and algebras with translation invariant (except, maybe , finite number) defining relationships. As an illustration of this method, we give one approach to the construction of linear representations of braid group and derive some series of such representations. Some invariants of oriented knots and links are constructed. The author is grateful to Yuri Drozd, Sergey Ovsienko and other members of algebraic seminar at Kiev University for the creative atmosphere without which this work could hardly appear.