Abstract
We compute the first differential cohomology of the affine Lie superalgebra \(\mathfrak {aff}(n|1)\) with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the (1, n)-dimensional real superspace. We also compute the same, but \(\mathfrak {aff}(n-1|1)\)-relative cohomology. We explicitly give 1-cocycles spanning these cohomology groups.
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Acknowledgements
We would like to thank Valentin Ovsienko, Claude Roger, Dimitry Leites, Mabrouk Ben Ammar and Christian Duval for their interest in this work.
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Ben Fraj, N., Faidi, T., Khalfoun, H. et al. Cohomology of \(\mathfrak {aff}(n|1)\) acting on the spaces of linear differential operators on the superspace \(\mathbb {R}^{1|n}\). Period Math Hung 80, 1–14 (2020). https://doi.org/10.1007/s10998-019-00304-2
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DOI: https://doi.org/10.1007/s10998-019-00304-2