Bull. Korean Math. Soc. 2019; 56(1): 13-22
Online first article January 14, 2019 Printed January 1, 2019
https://doi.org/10.4134/BKMS.b170774
Copyright © The Korean Mathematical Society.
Imed Basdouri, Ammar Derbali, Soumaya Saidi
Facult\'e des Sciences de Gafsa; Universit\'e de Gafsa; Universit\'e de Gafsa
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
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd