Commutative restricted Lie algebras (original) (raw)

This paper investigates commutative restricted Lie algebras, their properties, and their significance in the theory of simple restricted Lie algebras. A primary focus is the characterization of these algebras, particularly regarding their structure when they exhibit commutativity and how they relate to Cartan subalgebras. Key results include demonstrating that simple restricted commutative Lie algebras over algebraically closed fields are one-dimensional, revealing only two non-isomorphic types of such algebras.