- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Second cohomology of $\mathfrak{aff}(1)$ acting on $n$-ary differential operators Bull. Korean Math. Soc. 2019 Vol. 56, No. 1, 13-22 https://doi.org/10.4134/BKMS.b170774Published 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 Full-Text :