Lattices of subrepresentations of Lie algebras and their isomorphisms

To obtain the representation (L, R) of Lie algebras over the ring Λ, we construct the lattice of subrepresentations ℒ(L, R). Relations between the algebras L and R and the lattice ℒ(L, R) are studied. It turns out that in some cases the isomorphism of the lattice ℒ(L, R) can be continued so as to obtain a wider sublattice ℒ(LλR) consisting of subalgebras of a semidirect product LλR. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 46, Algebra, 2007.