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
Framization and deframization / Aicardi, Francesca; Juyumaya, Jesus; Papi, Paolo. - In: ALGEBRAS AND REPRESENTATION THEORY. - ISSN 1386-923X. - (2025). [10.1007/s10468-025-10341-w]
Framization and deframization
Paolo Papi
2025
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| File | Dimensione | Formato | |
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