The monoid structure of singular twisted virtual braids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912230923042816 |
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| author | Madeti, Prabhakar Negi, Komal |
| author_facet | Madeti, Prabhakar Negi, Komal |
| contents | In this paper, we examine specific submonoids within the singular twisted virtual braid monoid $STVB_n$. Notably, we establish that the singular twisted virtual pure braid monoid $STVP_n$ serves as the kernel of an epimorphism from $STVB_n$ onto the symmetric group $S_n$. We identify the generators and defining relations for $STVP_n$. Additionally, we construct other epimorphisms from $STVB_n$ onto $S_n$, whose kernels are analogous to $STVP_n$, and determine their respective generators and defining relations. Furthermore, we demonstrate the embedding of the monoid $STVB_n$ into a group. Also, we provide the extension of the representation of the twisted virtual braid group to the representation of the singular twisted virtual braid monoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The monoid structure of singular twisted virtual braids Madeti, Prabhakar Negi, Komal Group Theory Geometric Topology 57M50, 57K12, 20M32 In this paper, we examine specific submonoids within the singular twisted virtual braid monoid $STVB_n$. Notably, we establish that the singular twisted virtual pure braid monoid $STVP_n$ serves as the kernel of an epimorphism from $STVB_n$ onto the symmetric group $S_n$. We identify the generators and defining relations for $STVP_n$. Additionally, we construct other epimorphisms from $STVB_n$ onto $S_n$, whose kernels are analogous to $STVP_n$, and determine their respective generators and defining relations. Furthermore, we demonstrate the embedding of the monoid $STVB_n$ into a group. Also, we provide the extension of the representation of the twisted virtual braid group to the representation of the singular twisted virtual braid monoid. |
| title | The monoid structure of singular twisted virtual braids |
| topic | Group Theory Geometric Topology 57M50, 57K12, 20M32 |
| url | https://arxiv.org/abs/2502.08965 |