Locally finite-dimensional Lie algebras and their derivation algebras (Q1969647)

The paper deals with locally finite dimensional locally simple Lie algebras over a field of characteristic 0. Suppose the Lie algebra \(L\) is the direct limit of diagonally embedded Lie algebras and \(\text{Outder}(L)\) is an outer derivation algebra for \(L\). For every locally finite dimensional Lie algebra \(G\) of countable dimension the author constructs diagonal embeddings such that \(G\) is isomorphic to a subalgebra of \(\text{Outder}(L)\). Moreover, \(\text{Outder}(L)\) is not locally finite dimensional and has uncountable dimension.