SERIALLY COALESCENT CLASSES OF LIE ALGEBRAS

We introduce the concept of serially coalescent classes of Lie algebras corresponding to those of coalescent classes and ascendantly coalescent classes. We show that the class of finite-dimensional and nilpotent, the class of finite-dimensional and the class of finite-dimensional and soluble Lie algebras, are serially coalescent classes for locally finite Lie algebras over any field of characteristic zero. We also introduce the concept of locally serially coalescent classes of Lie algebras and find some locally serially coalescent classes for locally finite Lie algebras.