Simple Harish-Chandra modules over the superconformal current algebra
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_ | 1866916631162126336 |
|---|---|
| author | He, Y. Liu, D. Wang, Y. |
| author_facet | He, Y. Liu, D. Wang, Y. |
| contents | In this paper, we classify the simple Harish-Chandra modules over the superconformal current algebra $\widehat{\frak g}$, which is the semi-direct sum of the $N=1$ superconformal algebra with the affine Lie superalgebra $\dot{\frak g} \otimes \mathcal{A}\oplus \mathbb CC_1$, where $\dot{\frak g}$ is a finite-dimensional simple Lie algebra, and $\mathcal{A}$ is the tensor product of the Laurent polynomial algebra and the Grassmann algebra. As an application, we can directly get the classification of the simple Harish-Chandra modules over the $N=1$ Heisenberg-Virasoro algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19139 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple Harish-Chandra modules over the superconformal current algebra He, Y. Liu, D. Wang, Y. Representation Theory In this paper, we classify the simple Harish-Chandra modules over the superconformal current algebra $\widehat{\frak g}$, which is the semi-direct sum of the $N=1$ superconformal algebra with the affine Lie superalgebra $\dot{\frak g} \otimes \mathcal{A}\oplus \mathbb CC_1$, where $\dot{\frak g}$ is a finite-dimensional simple Lie algebra, and $\mathcal{A}$ is the tensor product of the Laurent polynomial algebra and the Grassmann algebra. As an application, we can directly get the classification of the simple Harish-Chandra modules over the $N=1$ Heisenberg-Virasoro algebra. |
| title | Simple Harish-Chandra modules over the superconformal current algebra |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2502.19139 |