Lie polynomials in a $q$-deformed universal enveloping algebra of a low-dimensional Lie algebra
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915166909628416 |
|---|---|
| author | Cantuba, Rafael Reno S. Merciales, Mark Anthony C. |
| author_facet | Cantuba, Rafael Reno S. Merciales, Mark Anthony C. |
| contents | The nonabelian two-dimensional Lie algebra over a field $\mathbb{F}$ has a presentation by generators $A$, $B$ and relation $\left[ A,B\right]=A$, with the universal enveloping algebra having a presentation by generators $A$, $B$ and relation $AB-BA=A$. A well-known fact is that the said Lie algebra is isomorphic to that which has a universal enveloping algebra that has a presentation by generators $A$, $B$ and relation $AB-BA=B$. Given $q,r,s\in\mathbb{F}$, solutions to the Lie polynomial characterization problems in the corresponding $q$-deformed universal enveloping algebras, with generalized relations $AB-qBA=rA$ and $AB-qBA=sB$, respectively, are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lie polynomials in a $q$-deformed universal enveloping algebra of a low-dimensional Lie algebra Cantuba, Rafael Reno S. Merciales, Mark Anthony C. Rings and Algebras 17B37 (Primary) 17B30, 16S15 (Secondary) The nonabelian two-dimensional Lie algebra over a field $\mathbb{F}$ has a presentation by generators $A$, $B$ and relation $\left[ A,B\right]=A$, with the universal enveloping algebra having a presentation by generators $A$, $B$ and relation $AB-BA=A$. A well-known fact is that the said Lie algebra is isomorphic to that which has a universal enveloping algebra that has a presentation by generators $A$, $B$ and relation $AB-BA=B$. Given $q,r,s\in\mathbb{F}$, solutions to the Lie polynomial characterization problems in the corresponding $q$-deformed universal enveloping algebras, with generalized relations $AB-qBA=rA$ and $AB-qBA=sB$, respectively, are presented. |
| title | Lie polynomials in a $q$-deformed universal enveloping algebra of a low-dimensional Lie algebra |
| topic | Rings and Algebras 17B37 (Primary) 17B30, 16S15 (Secondary) |
| url | https://arxiv.org/abs/2502.16074 |