Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.05721 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- This paper consists of two parts. In the first part, we prove that when $\mathfrak{g}$ is a simple basic Lie superalgebra with a principal odd nilpotent element $f$, the W-algebra $W^k(\mathfrak{g}, F)$ for $F=-\frac{1}{2}[f,f]$ is isomorphic to the SUSY W-algebra $W^k(\bar{\mathfrak{g}},f)$ via screening operators, which implies the supersymmetry of $W^k(\mathfrak{g}, F)$. In the second part, we show that a finite SUSY W-algebra, which is a Hamiltonian reduction of $U(\widetilde{\mathfrak{g}})$ for the SUSY Takiff algebra $\widetilde{\mathfrak{g}}=\mathfrak{g}\otimes \wedge(θ)$ is isomorphic to the Zhu algebra of a SUSY W-algebra. As a corollary, we show that a finite SUSY principal W-algebra is isomorphic to a finite principal W-algebra.