Automorphisms and primitive elements of free lie superalgebras

Abstract

We consider images of primitive elements of free color Lie (p-)su per algebras under endomorphisms of these algebras Web prove that endomorphisms preserving primitivity of elements are automorphisms (Theorem 4). Note that for free groups this problem was discussed in [10], Problem 2a. At the same time we show that it is not true if we consider only images of linear combinations of elements from free generatig set (see Example, Theorem 5). We formulate some open questions. In Section 1 we give necessary definitions and collect preliminary results. In Section 2 we prove main theorems. The results of this article were presented at algebraic semi­nars of Moscow State University.