Quantum Berezinian for the Twisted Super Yangian
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916561084743680 |
|---|---|
| author | Lin, Hongda Wang, Yongjie Zhang, Honglian |
| author_facet | Lin, Hongda Wang, Yongjie Zhang, Honglian |
| contents | Motivated by an open problem proposed in Molev's book \cite[Section 2.16, Example 16]{Mo07}, we investigate the quantum Berezinian $\mathfrak{B}^{tw}(u)$ associated with the twisted super Yangian, which is a coideal sub-superalgebra of the super Yangian of the general linear Lie superalgebra. We provide an explicit formulation of $\mathfrak{B}^{tw}(u)$, and we also construct the center of the twisted super Yangian. This construction enables us to define the special twisted super Yangian, which is isomorphic to the quotient of the twisted super Yangian by its center. Moreover, we demonstrate the quantum Sylvester theorem for both the generator matrix and the quantum Berezinian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Berezinian for the Twisted Super Yangian Lin, Hongda Wang, Yongjie Zhang, Honglian Quantum Algebra 17B37, 17D10, 20G42 Motivated by an open problem proposed in Molev's book \cite[Section 2.16, Example 16]{Mo07}, we investigate the quantum Berezinian $\mathfrak{B}^{tw}(u)$ associated with the twisted super Yangian, which is a coideal sub-superalgebra of the super Yangian of the general linear Lie superalgebra. We provide an explicit formulation of $\mathfrak{B}^{tw}(u)$, and we also construct the center of the twisted super Yangian. This construction enables us to define the special twisted super Yangian, which is isomorphic to the quotient of the twisted super Yangian by its center. Moreover, we demonstrate the quantum Sylvester theorem for both the generator matrix and the quantum Berezinian. |
| title | Quantum Berezinian for the Twisted Super Yangian |
| topic | Quantum Algebra 17B37, 17D10, 20G42 |
| url | https://arxiv.org/abs/2501.05800 |