2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152525Semi-infinite cohomology is constructed from scratch as the proper generalization of finite dimensional Lie algebra cohomology. The differential d and other operators are realized as universal inner deri- vations of a completed algebra, which acts on any appropriate semi-infinite complex. In particular, d is shown to be the unique derivation satisfying the "Cartan identity" and certain natural degree conditions. The proof that d is square-zero may well be the shortest (arguably, the only) one in print.19 pages (to appear in Journal of Algebra)High Energy Physics - TheoryQuantum Algebratext