The second cohomology spaces $\mathcal{K}(2)$ with coefficents in the superspace of weighted densities

• Date: 2020
• Main Authors: Basdouri, O., Braghtha , A., Hammami , S., O., A., S.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6030
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 515.1 Over the $(1,2)$-dimensional supercircle, we investigate the second cohomology space associated the lie superalgebra $\mathcal{K}(2)$ of vector fields on the supercircle $S^{1|2}$ with coefficients in the space of weighted densities. We explicitly give 2-cocycle spanning these cohomology s...