| Title:
|
Symmetries in connected graded algebras and their PBW-deformations (English) |
| Author:
|
Xu, Yongjun |
| Author:
|
Zhang, Xin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
73 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
1255-1272 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We focus on connected graded algebras and their PBW-deformations endowed with additional symmetric structures. Many well-known algebras such as negative parts of Drinfeld-Jimbo's quantum groups, cubic Artin-Schelter algebras and three-dimensional Sklyanin algebras appear in our research framework. As an application, we investigate a $\mathcal {K}_2$ algebra $\mathcal {A}$ which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra $\mathcal {FK}_3$, and explicitly construct all the (self-)symmetric and sign-(self-)symmetric PBW-deformations of $\mathcal {A}$. (English) |
| Keyword:
|
connected graded algebra |
| Keyword:
|
PBW-deformation |
| Keyword:
|
self-symmetry |
| Keyword:
|
sign-symmetry |
| Keyword:
|
$\mathcal {K}_2$ algebra |
| MSC:
|
16S80 |
| idZBL:
|
Zbl 07790572 |
| DOI:
|
10.21136/CMJ.2023.0511-22 |
| . |
| Date available:
|
2023-11-23T12:27:40Z |
| Last updated:
|
2026-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151958 |
| . |
| Reference:
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