Invariants of $\boldsymbol B$-Type Links via an Extension of the Kauffman Bracket

In this paper we find a method for constructing solid torus (or: $\boldsymbol B$-type) link invariants by means of extension of the Kauffman bracket for such links. This method can be viewed as the combination of the ideas proposed in [5, 7] and [8] with $\boldsymbol B$-type braid group theoretic approach to solid torus links which is given in [18]. Such method is shown to be compatible with skein relations of $\boldsymbol B$–type and leads to state sum expression for link invariant (in the case of the special diagrams).