Universal graded Lie algebras

Abstract For a given negatively graded Lie algebra K − , the universal graded Lie algebra U of type K − is defined and its existence proved. By posing additional conditions on K − , other types of universal graded Lie algebras are defined and discussed. The concept of universal graded Lie algebra leads naturally to the graded Cartan type Lie algebras. In fact, all graded Cartan type Lie algebras can be characterized as certain types of universal graded Lie algebras.