Framization and Deframization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914348508643328 |
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| author | Aicardi, Francesca Juyumaya, Jesús Papi, Paolo |
| author_facet | Aicardi, Francesca Juyumaya, Jesús Papi, Paolo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Framization and Deframization Aicardi, Francesca Juyumaya, Jesús Papi, Paolo Rings and Algebras Combinatorics General Topology 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. |
| title | Framization and Deframization |
| topic | Rings and Algebras Combinatorics General Topology |
| url | https://arxiv.org/abs/2405.10809 |