English

Framization and Deframization

Rings and Algebras 2026-02-26 v4 Combinatorics General Topology

Abstract

Starting from the geometric construction of the framed braid group, we define and study the framization of several Brauer-type monoids and also the set partition monoid, all of which appear in knot theory. We introduce the concept of deframization, which is a procedure to obtain a tied monoid from a given framed monoid. Furthermore, we show in detail how this procedure works on the monoids mentioned above. We also discuss the framization and deframization of some algebras, which are deformations, respectively, of the framized and deframized monoids discussed here.

Keywords

Cite

@article{arxiv.2405.10809,
  title  = {Framization and Deframization},
  author = {Francesca Aicardi and Jesús Juyumaya and Paolo Papi},
  journal= {arXiv preprint arXiv:2405.10809},
  year   = {2026}
}

Comments

Latex file, 41 pages, minor revision, final version, to appear in Algebras and Representation Theory