Analogs of Bol operators on superstrings
| Autor: | Sofiane Bouarroudj, Dimitry Leites, Irina Shchepochkina |
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| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Differential Geometry
Differential Geometry (math.DG) Computer Science::Information Retrieval General Mathematics Mathematics::Rings and Algebras FOS: Mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::General Literature Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Representation Theory (math.RT) Mathematics::Representation Theory Mathematics - Representation Theory |
| Zdroj: | International Journal of Algebra and Computation. 32:807-835 |
| ISSN: | 1793-6500 0218-1967 |
| DOI: | 10.1142/s0218196722500345 |
| Popis: | 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. Comment: 23 pages |
| Databáze: | OpenAIRE |
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