On invariants of the action of a finite group on a free Lie algebra.
Given a principal ideal domain of characteristic zero, containing , and a connected differential non-negatively graded free finite type -module , we prove that the natural arrow is an isomorphism of graded Lie algebras over , and deduce thereby that the natural arrow is an isomorphism of graded cocommutative Hopf algebras over ; as usual, stands for free part, for homology, for free Lie algebra, and for universal enveloping algebra. Related facts and examples are also considered....
2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Fm be the free metabelian Lie algebra of rank m over a field K of characteristic 0. We consider the semigroup IE(Fm) of the endomorphisms of Fm which are identical modulo the commutator ideal of Fm. We describe the factor semigroup of IE(Fm) modulo the congruence induced by the group of inner automorphisms.