Complex finitary simple Lie algebras (Q1291133)

Let \(K\) be algebraically closed field of characteristic zero, \(V\) be a vector space over \(K\) and \({\mathfrak {gl}}(V)\) be the Lie algebra of linear transformations of \(V\). \(f\in {\mathfrak{gl}}(V)\) is called finitary if \(\dim fV<\infty\). Finitary transformations form an ideal of \({\mathfrak{gl}}(V)\) and any subalgebra of this ideal is called finitary. The author classifies finitary simple Lie algebras over \(K\) and concludes that any such algebra is isomorphic to a special transvection algebra, a finitary orthogonal algebra or a finitary symplectic algebra.