  We demonstrate how a simple linear-algebraic technique used earlier to
compute low-degree cohomology of current Lie algebras, can be utilized to
compute other kinds of structures on such Lie algebras, and discuss further
generalizations, applications, and related questions. While doing so, we touch
upon such seemingly diverse topics as associative algebras of infinite
representation type, Hom-Lie structures, Poisson brackets of hydrodynamic type,
Novikov algebras, simple Lie algebras in small characteristics, and Koszul dual
operads.
