Abstrakt
This note is based on a short talk presented at the "42nd Win-ter School Geometry and Physics" held in Srni, Czech Republic, January 15th-22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting.
In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-sup eralgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational method to determine the cohomology groups induced by sub-sup eralgebras.
In particular, we show as an example the case of osp(1 | 4) and choose osp(1 | 2) xsp(2) as sub-algebra. We finally comment on some physical applications of such new cohomology classes related to sup er-branes.
The note is a compact version of [10].