Locally semisimple and maximal subalgebras of the finitary Lie algebras gl(∞), sl(∞), so(∞), and sp(∞)

We describe all locally semisimple subalgebras and all maximal subalgebras of the finitary Lie algebras gl(infinity), sl(infinity), so(infinity), and sp(infinity). For simple finite-dimensional Lie algebras these classes of subalgebras have been described in the classical works of A. Malcev and E. Dynkin. (C) 2009 Elsevier Inc. All rights reserved.