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

• DOI: 10.48550/arxiv.1702.03922
• Publication Date: 2017-01-01
• Authors: Zerui Zhang; L. A. Bokut; Yuqun Chen
• Keywords: Superalgebra; Novikov self-consistency principle; Supermatrix; Lie superalgebra; Associative property; Basis (linear algebra)

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