  The article is devoted to some ``strange'' phenomena of representation theory
and their interrelations. Cross-projective representations of pairs of
anticommutative algebras, alloys, their universal envelopping Lie algebras and
their representations, quaternary algebras and their alloyability are
discussed. Considered examples allow to conclude that new representations have
some intriguing features (continuous moduli of finite-dimensional irreducible
representations, sophisticated Clebsch-Gordan coefficient calculus, etc.).
