On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909724184674304 |
|---|---|
| author | Keshari, Vaibhav Nasser, Mohamad N. Prabhakar, Madeti |
| author_facet | Keshari, Vaibhav Nasser, Mohamad N. Prabhakar, Madeti |
| contents | This paper classifies complex homogeneous $2$-local representations of the multiple virtual braid group $M_kVB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, showing that such representations fall into exactly $2^{k+1}+1$ distinct types, out of which except three all are unfaithful. In addition, this paper investigates complex homogeneous $2$-local representations of the multiple welded braid group $M_kWB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, identifying $3 \cdot 2^{k-1} +1$ representations. Moreover, the article includes a construction of a non-local representation of $M_2WB_3$ that extends the known LKB representation of the braid group on $3$ strands, namely $B_3$, making a path towards constructing non-local representations of $M_kWB_n$ in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$ Keshari, Vaibhav Nasser, Mohamad N. Prabhakar, Madeti Representation Theory General Topology 57K12, 20C99 This paper classifies complex homogeneous $2$-local representations of the multiple virtual braid group $M_kVB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, showing that such representations fall into exactly $2^{k+1}+1$ distinct types, out of which except three all are unfaithful. In addition, this paper investigates complex homogeneous $2$-local representations of the multiple welded braid group $M_kWB_n$ into $\mathrm{GL}_n(\mathbb{C})$ for $n\geq3$ and $k >1$, identifying $3 \cdot 2^{k-1} +1$ representations. Moreover, the article includes a construction of a non-local representation of $M_2WB_3$ that extends the known LKB representation of the braid group on $3$ strands, namely $B_3$, making a path towards constructing non-local representations of $M_kWB_n$ in general. |
| title | On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$ |
| topic | Representation Theory General Topology 57K12, 20C99 |
| url | https://arxiv.org/abs/2508.04168 |