Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Second cohomology of $\mathfrak{aff}(1)$ acting on $n$-ary differential operators

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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