Translative isomorphisms and left-symmetric structures on \(W(m,{\mathbf n})\)
The author investigates translative isomorphisms of the Cartan-type Lie algebra \(W=W(m,{\mathbf n})\), i.e. isomorphisms of \(W\) into \(W'\dot+{\mathfrak {gl}} (m,{\mathfrak A})\) where \({\mathfrak A}={\mathfrak A}(m,{\mathbf n})\) is the divided power algebra on which \(W\) acts. For some such isomorphisms there is an associated left-symmetric structure on \(W\). The author shows that for a base field of characteristic \(p>0,\) \(W\) admits left-symmetric structures, and furthermore that \(W(m,\mathbf{1})\) admits restricted left-symmetric structures.
scientific article; zbMATH DE number 930158