Analogs of Bol operators on superstrings
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917774992867328 |
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| author | Bouarroudj, Sofiane Leites, Dimitry Shchepochkina, Irina |
| author_facet | Bouarroudj, Sofiane Leites, Dimitry Shchepochkina, Irina |
| contents | The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On the $1|n$-dimensional supermanifold (superstring) $\mathcal{M}$, we classify analogs of Bol operators invariant under the simple maximal subalgebra $\mathfrak{h}$ of the same rank as its simple ambient superalgebra $\mathfrak{g}$ of vector fields on $\mathcal{M}$ and containing all elements of negative degree of $\mathfrak{g}$ in a $\mathbb{Z}$-grading. We also consider the Lie superalgebras of vector fields $\mathfrak{g}$ preserving a contact structure on the superstring $\mathcal{M}$. We have discovered many new operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_10504 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Analogs of Bol operators on superstrings Bouarroudj, Sofiane Leites, Dimitry Shchepochkina, Irina Representation Theory Differential Geometry The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On the $1|n$-dimensional supermanifold (superstring) $\mathcal{M}$, we classify analogs of Bol operators invariant under the simple maximal subalgebra $\mathfrak{h}$ of the same rank as its simple ambient superalgebra $\mathfrak{g}$ of vector fields on $\mathcal{M}$ and containing all elements of negative degree of $\mathfrak{g}$ in a $\mathbb{Z}$-grading. We also consider the Lie superalgebras of vector fields $\mathfrak{g}$ preserving a contact structure on the superstring $\mathcal{M}$. We have discovered many new operators. |
| title | Analogs of Bol operators on superstrings |
| topic | Representation Theory Differential Geometry |
| url | https://arxiv.org/abs/2110.10504 |