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 $\ne 2$. 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

References in corpus (1)

• On free Gelfand-Dorfman-Novikov-Poisson algebras and a PBW theorem