On Lie-admissible algebras whose commutator Lie algebras are Lie subalgebras of prime associative algebras
An algebra \(D\) is called third power associative in case \((xx)x=x(xx)\) for all \(x\in D\). The authors describe third power associative multiplications \(*\) on noncentral Lie ideals of prime associative algebras and skew elements of prime algebras with involution provided that \(x*y-y*x=[x,y]\) for all \(x,y\) and the prime algebras in question do not satisfy polynomial identities of low degree. The authors also obtain necessary and sufficient conditions for these multiplications to be fourth power associative or flexible.
scientific article; zbMATH DE number 1556975
scientific article