TY - JOUR AU - M. Boujelben PY - 2022/07/07 Y2 - 2024/03/29 TI - First cohomology space of the orthosymplectic Lie superalgebra $\mathfrak{osp}(n|2)$ in the Lie superalgebra of superpseudodifferential operators JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 74 IS - 6 SE - Research articles DO - 10.37863/umzh.v74i6.6052 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6052 AB - 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)]. ER -