Nonlinear ξ-bi-skew Lie derivations on prime *-algebras

Key Points

• The research investigates conditions under which a certain map on a prime *-algebra acts as a Lie derivation.
• Defined a map on a unital prime *-algebra with a nontrivial projection.
• Verified conditions for the map to satisfy specific Lie derivation properties.
• Utilized algebraic identities involving the map and elements of the algebra.
• Proved that the defined map is an additive ?-derivation.
• Established necessary and sufficient conditions for the map involving elements of the algebra.