Lie type quotients of the maximal unipotent subgroup of Kac-Moody groups of type $\mathrm{HB}_{2}^{(2)}$
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912532512374784 |
|---|---|
| author | Corveleyn, Robynn |
| author_facet | Corveleyn, Robynn |
| contents | In this article, we construct infinite families $(G_n)_{n \in \mathbb{N}}$ of finite simple groups $G_n$ of Lie type, such that the rank of $G_n$ strictly increases as $n$ tends to infinity, and such that each $G_n$ is a quotient of the maximal unipotent subgroup $U^+$ of the (minimal) Kac-Moody group $\mathfrak{G}_{A}(\mathbb{K})$ of type $\mathrm{HB}_{2}^{(2)}$ over a finite field $\mathbb{K}$. Moreover, we show that the quotient maps lead to the construction of an infinite family of bounded degree spectral high-dimensional expanders. These provide the first class of examples of infinite families of high-dimensional expanders constructed from Lie type groups of unbounded rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie type quotients of the maximal unipotent subgroup of Kac-Moody groups of type $\mathrm{HB}_{2}^{(2)}$ Corveleyn, Robynn Group Theory 20G44, 20E26, 20D06, 05C48 In this article, we construct infinite families $(G_n)_{n \in \mathbb{N}}$ of finite simple groups $G_n$ of Lie type, such that the rank of $G_n$ strictly increases as $n$ tends to infinity, and such that each $G_n$ is a quotient of the maximal unipotent subgroup $U^+$ of the (minimal) Kac-Moody group $\mathfrak{G}_{A}(\mathbb{K})$ of type $\mathrm{HB}_{2}^{(2)}$ over a finite field $\mathbb{K}$. Moreover, we show that the quotient maps lead to the construction of an infinite family of bounded degree spectral high-dimensional expanders. These provide the first class of examples of infinite families of high-dimensional expanders constructed from Lie type groups of unbounded rank. |
| title | Lie type quotients of the maximal unipotent subgroup of Kac-Moody groups of type $\mathrm{HB}_{2}^{(2)}$ |
| topic | Group Theory 20G44, 20E26, 20D06, 05C48 |
| url | https://arxiv.org/abs/2508.08070 |