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

Abstract

We describe all locally semisimple subalgebras and all maximal subalgebras of the finitary Lie algebras $\gl(\infty), \sl(\infty), \so(\infty)$, and $\sp(\infty)$. For simple finite--dimensional Lie algebras these classes of subalgebras have been described in the classical works of A. Malcev and E. Dynkin. Key words (2000 MSC): 17B05 and 17B65.

References in corpus (1)

• Cartan subalgebras of root-reductive Lie algebras