Leicester Pure Maths Seminar, 21/10/2010
Abstract: Diagonal Lie algebras are deﬁned as the direct limits of ﬁnite-dimensional Lie algebras under diagonal injective homomorphisms. An explicit description of the isomorphism classes of diagonal locally simple Lie algebras was given by Baranov and Zhilinskii. Dimitrov and Penkov described all locally semisimple subalgebras of ﬁnitary inﬁnite-dimensional Lie algebras sl(\infty), so(\infty), and sp(\infty), which are important examples of diagonal locally simple Lie algebras. We extend these results further to the class of diagonal locally simple Lie algebras. In particular, all locally simple Lie subalgebras of any diagonal locally simple Lie algebra are described up to isomorphism.