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 Mat. Zametki, 2012, Volume 92, Issue 3, Pages 331–342 (Mi mz8667)

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

DOI: https://doi.org/10.4213/mzm8667

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

Bibliographic databases:

UDC: 512.73

Citation: N. Ben Fraj, M. Boujelbene, “Cohomology of $\mathfrak {osp}(2|2)$ Acting on Spaces of Linear Differential Operators on the Superspace $\mathbb{R}^{1|2}$”, Mat. Zametki, 92:3 (2012), 331–342; Math. Notes, 92:3 (2012), 302–311

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz8667
• https://doi.org/10.4213/mzm8667
• http://mi.mathnet.ru/eng/mz/v92/i3/p331

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This publication is cited in the following articles:
1. Ben Fraj N., Jabeur A., Safi I., “Cohomology of Osp(N Vertical Bar 2) Acting on the Spaces of Linear Differential Operators on the Superspace R-1 Vertical Bar N”, J. Lie Theory, 23:2 (2013), 575–587
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