The author first extends his results on the field of noncommutative separability, specially, strong separability. He shows that relative separability and split separability are dual notions when seen as special cases of the more general \(M\)-separability defined by K. Sugano [J. Fac. Sci., Hokkaido Univ., Ser. I 21, 196-208 (1971; Zbl 0236.16003)]. The author gives several results on strong separable extensions, some of the most important are: \(H\)-Galois extensions are strong separable extensions, where \(H\) is a finite dimensional, semisimple, cosemisimple Hopf algebra over a field \(K\); the endomorphism ring of a strong separable extension is also a strong separable extension with the same index; strong separable extensions have the same global dimension. He also provides several good illustrative examples.
The last section of the paper is devoted to link these algebraic extensions to results obtained using Jones polynomials. He shows, under several conditions on the ground ring, how to obtain the braid group representation and the Jones polynomial of oriented links by iterating the process done in the previous sections obtaining a tower of algebras from endomorphism rings of strongly separable extensions. – A good work on interdisciplinary research.