Representation theory of framisations of knot algebras (Q1697066)

This survey paper describes the structure and representation theory of various knot algebras, that is quotients of the group algebra of the braid group endowed with a Markov trace. The examples include the Yokonuma-Hecke algebra and its various generalizations and also the framization of the Temperley-Lieb algebra and its various generalizations. The results provide explicit combinatorial description for their simple modules, explicit formulae for dimensions of these simple modules, construction of bases and also semisimplicity criteria for algebras. For the entire collection see [Zbl 1387.00028].