Second cohomology of $\mathfrak{aff}(1)$ acting on $n$-ary differential operators
Bull. Korean Math. Soc. 2019 Vol. 56, No. 1, 13-22
Published online 2019 Jan 01
Imed Basdouri, Ammar Derbali, Soumaya Saidi
Facult\'e des Sciences de Gafsa; Universit\'e de Gafsa; Universit\'e de Gafsa
Abstract : We compute the second cohomology of the affine Lie algebra $\mathfrak{aff}(1)$ on the dimensional real space with coefficients in the space $\mathcal{D}^n_{\underline{\lambda},\mu}$ of $n$-ary linear differential operators acting on weighted densities where $\underline{\lambda}=(\lambda_1,\ldots,\lambda_n)$. We explicitly give $2$-cocycles spanning these cohomology.
Keywords : cohomology, affine Lie algebras, $n$-ary linear differential operat\-ors
MSC numbers : 17B56, 17B67, 53D55
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