On free Gelfand--Dorfman--Novikov superalgebras and a PBW type theorem

Abstract

We construct a linear basis of a free GDN superalgebra over a field of characteristic $\neq 2$. As applications, we prove a PBW theorem, that is, any GDN superalgebra can be embedded into its universal enveloping commutative associative differential superalgebra. An Engel theorem under some assumptions is given.

21 pages