First cohomology space of the orthosymplectic Lie superalgebra $\mathfrak{osp}(n|2)$ in the Lie superalgebra of superpseudodifferential operators
UDC 515.12 We investigate the first cohomology space associated with the embedding of the Lie orthosymplectic superalgebra $\mathfrak{osp}(n|2)$ on the $(1,n)$-dimensional superspace $\mathbb{R}^{1|n}$ in the Lie superalgebra $ \mathcal{S}\Psi\mathcal{DO}(n)$ (for $n \geq 4$ ) of superpseudodifferen...
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| Datum: | 2022 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6052 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 515.12 We investigate the first cohomology space associated with the embedding of the Lie orthosymplectic superalgebra $\mathfrak{osp}(n|2)$ on the $(1,n)$-dimensional superspace $\mathbb{R}^{1|n}$ in the Lie superalgebra $ \mathcal{S}\Psi\mathcal{DO}(n)$ (for $n \geq 4$ ) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we give explicit expressions of the basis cocycles.This work is the simplest generalization of a result by Basdouri [First space cohomology of the orthosymplectic Lie superalgebra in the Lie superalgebra of superpseudodifferential operators, Algebras and Representation Theory, 16, 35-50 (2013)]. |
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| DOI: | 10.37863/umzh.v74i6.6052 |