Principal SUSY and nonSUSY W-algebras and their Zhu algebras
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914143031787520 |
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| author | Genra, Naoki Song, Arim Suh, Uhi Rinn |
| author_facet | Genra, Naoki Song, Arim Suh, Uhi Rinn |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Principal SUSY and nonSUSY W-algebras and their Zhu algebras Genra, Naoki Song, Arim Suh, Uhi Rinn Mathematical Physics 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. |
| title | Principal SUSY and nonSUSY W-algebras and their Zhu algebras |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2502.05721 |