Cohomology of $\mathfrak {osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1}

Details Cohomology of $\mathfrak {osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1} Cohomology of $\mathfrak {osp}(1|2)$ acting on linear differential operators on the supercircle $S^{1|1}

2007-09-12

arxiv.org/abs/0709.1768v1

Letters in Mathematical Physics (2007) 81:239-251

Mathematics

Representation Theory

Scientific paper

10.1007/s11005-007-0181-z

We compute the first cohomology spaces $H^1(\mathfrak{osp}(1|2);\mathfrak{D}_{\lambda,\mu})$ ($\lambda, \mu\in\mathbb{R}$) of the Lie superalgebra $\mathfrak{osp}(1|2)$ with coefficients in the superspace $\mathfrak{D}_{\lambda,\mu}$ of linear differential operators acting on weighted densities on the supercircle $S^{1|1}$. The structure of these spaces was conjectured in \cite{gmo}. In fact, we prove here that the situation is a little bit more complicated. (To appear in LMP.)

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