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Cohomology of $$\mathfrak {aff}(n|1)$$aff(n|1) acting on the spaces of linear differential operators on the superspace $$\mathbb {R}^{1|n}$$R1|n
Periodica Mathematica Hungarica ( IF 0.6 ) Pub Date : 2019-12-09 , DOI: 10.1007/s10998-019-00304-2
N. Ben Fraj , T. Faidi , H. Khalfoun , Z. Abdelwaheb

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.

中文翻译:

$$\mathfrak {aff}(n|1)$$aff(n|1) 作用于超空间 $$\mathbb {R}^{1|n}$$R1| 上的线性微分算子空间的上同调n

我们计算仿射李超代数 \(\mathfrak {aff}(n|1)\) 的一阶微分上同调,其中线性微分算子的超空间中的系数作用于 (1, n) 维上的加权密度空间真正的超空间。我们也计算相同的,但 \(\mathfrak {aff}(n-1|1)\)-相对上同调。我们明确给出了跨越这些上同调群的 1-cocycle。
更新日期:2019-12-09
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