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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.05252 |
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| _version_ | 1866908941556908032 |
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| author | Aoi, Hisashi |
| author_facet | Aoi, Hisashi |
| contents | We analyze the triviality of inhomogeneous $γ$-deformations of the oscillator Lie superalgebra $B(0,n) = \mathfrak{osp}(1|2n)$. As the main theorem, we show that for $n \geq 2$, the $γ$-deformation is trivial if and only if all deformation parameters vanish. The proof is based on the explicit construction of $2n$ certificates (left null space vectors $c$ satisfying $c^\top A_μ= 0$ and $c^\top L_μ\neq 0$) for the structure constant matrices $A_μ$ of the coboundary operator. We provide a unified construction of certificates classified into three Families, and in particular clarify the geometric meaning of the coefficient $1 + δ_{n,2}$ that appears in the Family~III certificate. We also discuss the contrast with the exceptional case of $B(0,1) = \mathfrak{osp}(1|2)$ (where all deformations are trivial). As an appendix, we outline the computational verification performed using exact rational arithmetic over $\mathbb{Q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the triviality of inhomogeneous deformations of $\mathfrak{osp}(1|2n)$ Aoi, Hisashi Representation Theory 17B56 We analyze the triviality of inhomogeneous $γ$-deformations of the oscillator Lie superalgebra $B(0,n) = \mathfrak{osp}(1|2n)$. As the main theorem, we show that for $n \geq 2$, the $γ$-deformation is trivial if and only if all deformation parameters vanish. The proof is based on the explicit construction of $2n$ certificates (left null space vectors $c$ satisfying $c^\top A_μ= 0$ and $c^\top L_μ\neq 0$) for the structure constant matrices $A_μ$ of the coboundary operator. We provide a unified construction of certificates classified into three Families, and in particular clarify the geometric meaning of the coefficient $1 + δ_{n,2}$ that appears in the Family~III certificate. We also discuss the contrast with the exceptional case of $B(0,1) = \mathfrak{osp}(1|2)$ (where all deformations are trivial). As an appendix, we outline the computational verification performed using exact rational arithmetic over $\mathbb{Q}$. |
| title | On the triviality of inhomogeneous deformations of $\mathfrak{osp}(1|2n)$ |
| topic | Representation Theory 17B56 |
| url | https://arxiv.org/abs/2604.05252 |