First cohomology space of the orthosymplectic Lie superalgebra $\mathfrak{osp}(n|2)$ in the Lie superalgebra of superpseudodifferential operators

M.  Boujelben

doi:10.37863/umzh.v74i6.6052

M. Boujelben Univ. de Sfax, Tunisia https://orcid.org/0000-0002-5244-4477

DOI: https://doi.org/10.37863/umzh.v74i6.6052

Ключові слова: Cohomology, Orthosymplectic superalgebra, superpseudodifferential operators, Poisson superalgebra

Анотація

УДК 515.12

Простiр першої когомологiї ортосимплектичної супералгебри Лi $\mathfrak{osp}(n|2)$ у супералгебрi Лi суперпсевдодиференцiальних операторiв

Вивчається простiр першої когомологiї, пов’язаний з вкладенням ортосимплектичної супералгебри Лi $\mathfrak{osp}(n|2)$ на $(1, n)$-вимiрному суперпросторi $\mathbb{R}^{1|n}$ у супералгебрi Лi $ \mathcal{S}\Psi\mathcal{DO}(n)$ (для $n \geq 4$) суперпсевдодиференцiальних операторiв з гладкими коефiцiєнтами. Наслiдуючи Овсiєнка та Роджера, ми наводимо точнi вирази для базису коциклiв. Ця робота є найпростiшим узагальненням результату Basdouri[First space cohomology of the orthosymplectic Lie superalgebra in the Lie superalgebra of superpseudodifferential operators, Algebras and Representation Theory, 16, 35-50 (2013)].

Посилання

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