Cohomology of $\frak {osp}(1|2)$ acting on the space of bilinear differential operators on the superspace $\mathbb{R}^{1|1}$
Abstract
We compute the first cohomology of the ortosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ on the (1,1)-dimensional real superspace with coefficients in the superspace $\frak{D}_{\lambda,\nu;\mu}$ of bilinear differential operators acting on weighted densities. This work is the simplest superization of a result by Bouarroudj [Cohomology of the vector fields Lie algebras on $\mathbb{R}\mathbb{P}^1$ acting on bilinear differential operators, International Journal of Geometric Methods in Modern Physics (2005), {\bf 2}; N 1, 23-40].
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2009
- DOI:
- 10.48550/arXiv.0911.2769
- arXiv:
- arXiv:0911.2769
- Bibcode:
- 2009arXiv0911.2769B
- Keywords:
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- Mathematics - Representation Theory;
- 53D55
- E-Print:
- International Journal of Geometric Methods in Modern Physics, Vol. 9, No. 4 (2012) 1250033