Generalized electrical Lie algebras
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913894188974080 |
|---|---|
| author | Berenstein, Arkady Gainutdinov, Azat Gorbounov, Vassily |
| author_facet | Berenstein, Arkady Gainutdinov, Azat Gorbounov, Vassily |
| contents | We generalize the electrical Lie algebras originally introduced by Lam and Pylyavskyy in several ways. To each Kac-Moody Lie algebra $\mathfrak{g}$ we associate two types (vertex type and edge type) of the generalized electrical algebras. The electrical Lie algebras of vertex type are always subalgebras of $\mathfrak{g}$ and are flat deformations of the nilpotent Lie subalgebra of $\mathfrak{g}$. In many cases including $sl_n$, $so_n$, and $sp_{2n}$ we find new (edge) models for our generalized electrical Lie algebras of vertex type. Finding an edge model in general is an interesting an open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized electrical Lie algebras Berenstein, Arkady Gainutdinov, Azat Gorbounov, Vassily Representation Theory Rings and Algebras 2020: 14L40, 20G05, 82B20, 05E10 We generalize the electrical Lie algebras originally introduced by Lam and Pylyavskyy in several ways. To each Kac-Moody Lie algebra $\mathfrak{g}$ we associate two types (vertex type and edge type) of the generalized electrical algebras. The electrical Lie algebras of vertex type are always subalgebras of $\mathfrak{g}$ and are flat deformations of the nilpotent Lie subalgebra of $\mathfrak{g}$. In many cases including $sl_n$, $so_n$, and $sp_{2n}$ we find new (edge) models for our generalized electrical Lie algebras of vertex type. Finding an edge model in general is an interesting an open problem. |
| title | Generalized electrical Lie algebras |
| topic | Representation Theory Rings and Algebras 2020: 14L40, 20G05, 82B20, 05E10 |
| url | https://arxiv.org/abs/2405.02956 |