ABSTRACT
Certain key ingredients of Jones’ theory may be reduced to algebra in different ways. Subsequently, the Jones polynomial was generalized in different directions and several old problems of Tait's in knot theory were solved. For example, the Jones polynomial may be defined from certain traces of Ocneanu's on a sequence of finite dimensional algebras named after Hecke. In this paper the authors build from a small system of axioms, one being relative separability and another its module-theoretic dual notion of split extension, the Jones theory leading up to the VL polynomial for a link L. The structure theory of finite separable extensions of algebras, its relations with representation theory of groups, and the duality of separable and split extension is treated in the author paper. In the present paper the authors discusses a dimension question and what relation finite separability has with quasi-Frobenius extensions.
