Some examples of locally finite simple Lie algebras (Q1894894)

Families of locally finite dimensional simple Lie algebras are constructed, which can not be presented as direct limits of finite dimensional simple Lie algebras. This answers a question raised by \textit{R. K. Amayo} and \textit{I. Stewart} [``Infinite dimensional Lie algebras'', Leyden (1974; Zbl 0302.17006)]. For locally finite groups analogous examples exist, however, the proof needs very sophisticated methods. The present construction might give a hint how to find examples in the group case as well.