This article is cited in 2 papers

Cohomology of $\mathfrak {osp}(2|2)$ Acting on Spaces of Linear Differential Operators on the Superspace $\mathbb{R}^{1|2}$

N. Ben Fraj, M. Boujelbene

Institut Supérieur des Sciences Appliquées et de Technologie de Sousse

Abstract: We compute the first differential cohomology of the orthosymplectic Lie superalgebra $\mathfrak{osp}(2|2)$ with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the $(1,2)$-dimensional real superspace. We also compute the same, but $\mathfrak{osp}(1|2)$-relative, cohomology. We explicitly give $1$-cocycles spanning these cohomologies. This work is the simplest generalization of a result from [1].

Keywords: differential cohomology, orthosymplectic Lie superalgebra, differential operator, superspace, Lie algebra of contact vector fields.

UDC: 512.73

Received: 23.03.2012

DOI: 10.4213/mzm8667

 English version: Mathematical Notes, 2012, 92:3, 302–311

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