On braided Hopf structures on exterior algebras
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_ | 1866917106818220032 |
|---|---|
| author | Kashaev, Rinat Mangazeev, Vladimir |
| author_facet | Kashaev, Rinat Mangazeev, Vladimir |
| contents | We show that the exterior algebra of a vector space $V$ of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis.
A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang--Baxter equation. These solutions are conjectured to give rise to the two-variable Links--Gould polynomial invariants associated with the super-quantum group $U_q(\mathfrak{gl}(N|1))$, where $N = \dim(V)$. We support this conjecture through computations for small values of $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On braided Hopf structures on exterior algebras Kashaev, Rinat Mangazeev, Vladimir Quantum Algebra Mathematical Physics Geometric Topology Rings and Algebras 16T05 (Primary) 16T25, 16T30, 57K10, 57K14 (Secondary) We show that the exterior algebra of a vector space $V$ of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis. A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang--Baxter equation. These solutions are conjectured to give rise to the two-variable Links--Gould polynomial invariants associated with the super-quantum group $U_q(\mathfrak{gl}(N|1))$, where $N = \dim(V)$. We support this conjecture through computations for small values of $N$. |
| title | On braided Hopf structures on exterior algebras |
| topic | Quantum Algebra Mathematical Physics Geometric Topology Rings and Algebras 16T05 (Primary) 16T25, 16T30, 57K10, 57K14 (Secondary) |
| url | https://arxiv.org/abs/2505.15569 |